Document:

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                                                                     Exhibit 4.4

THE SECURITIES EVIDENCED HEREBY HAVE NOT BEEN REGISTERED OR QUALIFIED UNDER THE
SECURITIES ACT OF 1933, AS AMENDED, OR THE SECURITIES LAWS OF ANY STATE, AND MAY
BE OFFERED, SOLD, PLEDGED OR HYPOTHECATED ONLY IF REGISTERED AND QUALIFIED
PURSUANT TO THE RELEVANT PROVISIONS OF FEDERAL AND STATE SECURITIES LAWS OR IF
THE COMPANY IS PROVIDED AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE
COMPANY THAT REGISTRATION AND QUALIFICATION UNDER FEDERAL AND STATE SECURITIES
LAWS IS NOT REQUIRED OR IF THE COMPANY OTHERWISE SATISFIES ITSELF THAT
REGISTRATION IS NOT REQUIRED.

                   WARRANT TO PURCHASE SHARES OF COMMON STOCK

                                       OF

                               ALSIUS CORPORATION,
                            A CALIFORNIA CORPORATION

Date of Grant: April 30, 2003

     This certifies that for the purchase price paid, the undersigned holder of
this Warrant (the "Original Holder") and any person to whom the interest in this
Warrant is lawfully transferred (the Original Holder hereof and such transferees
referred to hereinafter as the "Holder"), is entitled to purchase up to that
number of shares of Common Stock (as hereinafter defined) as determined pursuant
to Section 1(b) hereof, pursuant to the terms of this Warrant. "Common Stock"
means the Common Stock of Alsius Corporation, a California corporation (the
"Company"). This Warrant is being issued in connection with a series of
convertible promissory notes issued by the Company on the Date of Grant of this
Warrant (such notes, together with and notes having substantially the same terms
that are later issued, the "Bridge Notes"). The Bridge Notes are automatically
convertible into preferred stock of the Company (the "Series F Preferred Stock")
upon a financing with certain triggering events (such financing triggering the
automatic conversion of the Bridge Notes, a "Qualified Financing").

     1. Exercise of Warrant.

          (a) Exercise Price; Aggregate Exercise Price. The exercise price at
which this Warrant may be exercised shall be equal to ten percent (10%) of the
price per share of Series F Preferred Stock paid in the Qualified Financing or,
if no Qualified Financing occurs prior to the earlier of (i) the maturity date
of the Bridge Notes (including any extension thereof in accordance with the
terms of the Bridge Notes) (the "Maturity Date") or (ii) the consummation of a
Sale Transaction (as defined in the Bridge Notes), the exercise price at which
this Warrant may be exercised shall be equal to $0.207 (the "Exercise Price").
The initial "Aggregate Exercise Price" will be the amount resulting from
multiplying the Exercise Price times the total number of shares of the Common
Stock that may be purchased upon exercise hereof.

          (b) Number of Shares. Subject to the exercisability restrictions set
forth in Section 1(c) hereof and as adjusted pursuant to Section 2 hereof, this
Warrant will entitle the

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Holder to purchase up to the number of shares of Common Stock equal to the
quotient obtained by dividing forty percent (40%) of the original principal
amount of the Holder's Bridge Note by the Series F Preferred Stock per share
price; provided, however, that if no Qualified Financing occurs prior to the
earlier of (i) the Maturity Date or (ii) the consummation of a Sale Transaction,
this Warrant will entitle the Holder to purchase up to the number of shares of
Common Stock equal to the quotient obtained by dividing forty percent (40%) of
the original principal amount of the Holder's Bridge Note by $2.07.

          (c) Exercise Period. This Warrant shall become exercisable on the
earliest to occur of (i) a Qualified Financing in which the Bridge Notes
automatically convert into Series F Preferred Stock, (ii) the Maturity Date and
(iii) immediately prior to a Sale Transaction, provided such exercise of this
Warrant shall be conditioned upon the closing of a Sale Transaction ("Exercise
Date"). This Warrant will be exercisable for a period of five (5) years from the
Exercise Date.

          (d) Method of Exercise; Payment. The purchase right represented by
this Warrant may be exercised by the Holder, in whole or in part, for up to the
total number of shares remaining available for exercise by the surrender of this
Warrant (with the notice of exercise form attached hereto as Annex I duly
executed) at the principal office of the Company and by payment to the Company,
by: (i) check made payable to the Company drawn on a United States bank and for
United States funds, (ii) delivery to the Company of evidence of cancellation of
indebtedness of the Company to such Holder, or (iii) any combination thereof, of
an amount in each case equal to the then applicable Exercise Price per share
multiplied by the number of shares of Common Stock then being purchased. Upon
partial exercise, the Company shall promptly issue an amended warrant
representing the remaining number of shares purchasable hereunder. All other
terms and conditions of such amended warrant shall be identical to those
contained herein, including, but not limited to the effective date hereof.

          (e) Net Exercise. In the event that the Company's Common Stock is then
traded on a national securities exchange or admitted to unlisted trading
privileges on such an exchange, or is listed on the National Market (the
"National Market") of the National Association of Securities Dealers Automated
Quotations System (the "Nasdaq") or other over-the-counter quotation system,
then the Holder may elect to receive, without the payment by the Holder of any
additional consideration, shares equal to the value of this Warrant, or any
portion hereof, by the surrender of this Warrant or such portion to the Company
(with the notice of exercise form attached hereto as Annex I duly executed).
Thereupon, the Company shall issue to the Holder such number of fully paid and
nonassessable shares of Common Stock as is computed using the following formula:

                     Y (A - B)
                     ---------
                 X =     A

          Where: X = The number of shares of Common Stock to be issued to the
                     Holder pursuant to this net exercise;

                 Y = The number of shares of Common Stock in respect of which
                     the net issue election is made;

                                      -2-

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                 A = The fair market value of one share of the Company's Common
                     Stock at the time the net issue election is made;

                 B = The Exercise Price in effect under this Warrant at the time
                     the net issuance election is made pursuant to this Section
                     1(e).

     For purposes of this Section 1(e), the fair market value of one share of
the Company's Common Stock as of a particular date shall be determined as
follows: (i) if traded on a securities exchange or through the Nasdaq National
Market, the value shall be deemed to be the average of the closing prices of the
securities on such exchange for the ten (10) trading days ending on the trading
day prior to the net exercise election; and (ii) if traded over-the-counter, the
value shall be deemed to be the average of the closing bid or sale prices
(whichever is applicable) for the ten (10) trading days ending on the trading
day prior to the net exercise.

          (f) Issuance of New Warrant. In the event of any exercise of the
purchase right represented by this Warrant, certificates for the shares of
Common Stock so purchased will be delivered to the Holder within fifteen (15)
business days after receipt of such payment and, unless this Warrant has been
fully exercised or has expired, a new warrant representing the portion of the
shares of Common Stock, if any, with respect to which this Warrant will not then
have been exercised will also be issued to the Holder within a fifteen (15)
business day period.

     2. Adjustment of Number and Kind of Securities and Adjustment of Exercise
Price. The number and kind of securities purchasable upon the exercise of this
Warrant, and the Exercise Price, will be subject to adjustment from time to time
upon the occurrence of certain events, as follows:

          (a) Reclassification, Reorganization, Consolidation or Merger. In case
of any reclassification of the Common Stock of the Company, or any
reorganization, consolidation or merger of the Company with or into another
corporation (other than a merger or reorganization with respect to which the
Company is the continuing corporation and which does not result in any
reclassification of the Common Stock), the Company, or such successor
corporation, as the case may be, will execute and deliver to the Holder a new
warrant in substitution for this Warrant which will provide that the Holder will
have the right to exercise such new warrant and upon such exercise to receive,
in lieu of each share of Common Stock issuable upon exercise of this Warrant,
the number and kind of securities, money and property receivable upon such
reclassification, reorganization, consolidation or merger by a holder of shares
of Common Stock of the Company for each share of Common Stock. Such new warrant
will provide for adjustments which will be as nearly equivalent as may be
practicable to the adjustments provided for in this Section 2 including, without
limitation, adjustments to the Exercise Price and to the number of shares
issuable upon exercise of this Warrant. The provisions of this Section 2(a) will
similarly apply to successive reclassifications, reorganizations, consolidations
or mergers.

          (b) Split, Subdivision or Combination of Shares. If the Company at any
time while this Warrant remains outstanding and unexpired splits, subdivides or
combines its Common Stock, the Exercise Price will be proportionately decreased
in the case of a split or subdivision or proportionately increased in the case
of a combination. Any adjustment under this Section 2(b) will become effective
when the split, subdivision or combination becomes effective.

                                      -3-

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          (c) Stock Dividends. If the Company at any time while this Warrant
remains outstanding and unexpired will pay a dividend with respect to the Common
Stock payable in shares of Common Stock, securities convertible into or
exchangeable for Common Stock ("Convertible Securities"), the Exercise Price
will be adjusted, from and after the date of determination of the shareholders
entitled to receive such dividend or distribution, to that price determined by
multiplying the Exercise Price in effect immediately prior to such date of
determination by a fraction (i) the numerator of which will be the total number
of shares of Common Stock outstanding immediately prior to such dividend or
distribution, and (ii) the denominator of which will be the total number of
shares of Common Stock outstanding immediately after such dividend or
distributions (including shares of Common Stock issuable upon exercise,
conversion or exchange of any Convertible Securities issued as a dividend or
distribution). If the Convertible Securities issued as such dividend or
distributions by their terms provided, with the passage of time or otherwise,
for any increase or decrease in the consideration payable to the Company, or any
increase or decrease in the number of shares issuable upon exercise, conversion
or exchange thereof any change of rate or otherwise), the Exercise Price will,
upon any such decrease or increase becoming effective, be reduced or increased
to reflect such decrease or increase as if such decrease or increase became
effective immediately prior to the issuance of the Convertible Securities as the
dividend or distribution. Any adjustment under this Section 2(c) will become
effective on the record date or, if there is not record date, on the date of
issuance.

          (d) Adjustment of Number of Shares. Upon each adjustment in the
Exercise Price pursuant to this Section 2, the number of shares issuable upon
exercise of this Warrant will be adjusted to the number obtained by dividing the
then outstanding Aggregate Exercise Price by the Exercise Price immediately
after such adjustment.

     3. Compliance With Securities Act; Transferability of Warrant.

          (a) Legends. Any certificate for shares issued upon exercise hereof
will be imprinted with a legend in substantially the form set forth in the
Notice of Exercise form attached hereto as Annex I.

          (b) Restricted Securities. The Holder understands that the Warrant and
the Common Stock that the Holder is purchasing are characterized as "restricted
securities" under the federal securities laws, inasmuch as they are being
acquired from the Company in a transaction not involving a public offering, and
that under such laws and applicable regulations such securities may be resold
without registration under the Securities Act of 1933, as amended (the "1933
Act") only in certain limited circumstances. In this connection, the Holder is
familiar with Rule 144, as presently in effect, and understands the resale
limitations imposed thereby and by the 1933 Act. The Holder understands Rule 144
is not currently available for the sale of the Common Stock and may never be so
available.

          (c) Transferability and Negotiability of Warrant. This Warrant may not
be transferred or assigned in whole or in part, unless (i) there is then in
effect a registration statement (declared effective by the Securities and
Exchange Commission (the "SEC") and necessary state regulatory authorities)
under the 1933 Act covering such proposed disposition and such disposition is
made in accordance with such registration statement; or (ii) the Holder

                                      -4-

<PAGE>

shall have notified the Company of the proposed disposition and shall have
furnished the Company with a brief statement of the circumstances surrounding
the proposed disposition, and if reasonably requested by the Company, the Holder
shall have furnished the Company with an opinion of counsel, reasonably
satisfactory to the Company that such disposition will not require registration
of such shares under the 1933 Act; provided however, no such registration or
opinion shall be necessary for any transfer of this Warrant: (i) in compliance
with Rule 144 or Rule 144A of the 1933 Act, (ii) by gift, will or intestate
succession by the Holder to his or her spouse or lineal descendants or ancestors
or any trust for any of the foregoing or (iii) pursuant to a transfer to any
partner, former partner, affiliate or the estate of any such partner of the
Holder; provided that, in each of the foregoing cases, the transferee agrees in
writing to be subject to the terms of this Warrant. Subject to the provisions of
this Section 3(c), title to this Warrant may be transferred in the same manner
as a negotiable instrument transferable by endorsement and delivery, by
execution and delivery of a completed Assignment Form attached hereto as Annex
II.

     4. Representations and Warranties of the Holder. The Holder hereby
represents and warrants that:

          (a) Authorization. The Holder has full power and authority to enter
into this Warrant, and this Warrant constitutes the valid and legally binding
obligations of the Holder, enforceable in accordance with its terms.

          (b) Purchase Entirely for Own Account. This Warrant and the Common
Stock issuable upon exercise of this Warrant (collectively, the "Securities")
will be acquired for investment for the Holder's own account, not as a nominee
or agent, and not with a view to the resale or distribution of any part thereof,
and the Holder has no present intention of selling, granting any participation
in or otherwise distributing the same. The Holder does not have any contract,
undertaking, agreement or arrangement with any person to sell, transfer or grant
participation in any of the Securities to such person or to any third person.

          (c) Disclosure of Information. The Holder believes that the Holder has
received all the information the Holder considers necessary or appropriate for
deciding whether to purchase this Warrant. The Holder has had an opportunity to
ask questions and receive answers from the Company regarding the terms and
conditions of the offering and sale of the Securities.

          (d) Investment Experience. The Holder is an investor in securities of
companies in the development stage and acknowledges that the Holder is able to
fend for himself and bear the economic risk of its investment, including the
complete loss thereof, and has such knowledge and experience in financial or
business matters that the Holder is capable of evaluating the merits and risks
of the investment in the Securities. The Holder acknowledges that the Company
currently is seeking investors to participate in a proposed offering of the
Company's securities, but there can be no assurances that the Company will find
financing on acceptable terms, if at all. The Holder has not been organized for
the purpose of acquiring the Securities.

                                      -5-

<PAGE>

          (e) Accredited Investor. The Holder is an "accredited investor" within
the meaning of Rule 501 of Regulation D, as presently in effect, promulgated
under the 1933 Act.

     5. Market Stand-Off Agreement. The Holder agrees, so long as the Holder
holds at least one percent (1%) of the Company's outstanding voting equity
securities, in connection with the Company's initial public offering of the
Company's securities that, upon request of the Company or the underwriters
managing any underwritten offering of the Company's securities, not to sell,
make any short sale of, loan, grant any option for the purchase of, or otherwise
dispose of any Common Stock of the Company (other than those included in the
registration) without the prior written consent of the Company or such
underwriters, as the case may be, for such period of time (not to exceed one
hundred eighty (180) days in the case of a Qualified IPO (as hereinafter
defined) and not to exceed ninety (90) days, or one hundred twenty (120) days if
the Holder holds ten percent (10%) of the outstanding stock of the Company, in
the case of any other public offering) from the effective date of such
registration as may be requested by the underwriters; provided, that all other
Holders of at least one percent (1%) of the Company's outstanding voting equity
securities and all of the officers and directors of the Company who own stock of
the Company also agree to such restrictions. A "Qualified IPO" shall mean a firm
underwritten public offering by the Company of its Common Stock, with net
proceeds of at least $20,000,000 and with a price per share of at least $4.80
(as adjusted for any stock splits, stock dividends, recapitalizations or the
like), prior to the deduction of underwriting commissions and offering expenses.

     6. Replacement of Warrant. On receipt of evidence reasonably satisfactory
to the Company of the loss, theft, destruction, or mutilation of this Warrant
and, in the case of loss, theft, or destruction, on delivery of an indemnity
agreement reasonably satisfactory in form and substance to the Company or, in
the case of mutilation, on surrender and cancellation of this Warrant, the
Company at its expense shall execute and deliver, in lieu of this Warrant, a new
warrant of like tenor and amount.

     7. Reservation of Stock. The Company covenants that during the term this
Warrant is exercisable, the Company will reserve from its authorized and
unissued Common Stock a sufficient number of shares to provide for the issuance
of Common Stock upon the exercise of this Warrant and, from time to time, will
take all steps necessary to amend its Certificate of Incorporation to provide
sufficient reserves of shares of Common Stock issuable upon exercise of the
Warrant. The Company agrees that its issuance of this Warrant shall constitute
full authority to its officers who are charged with the duty of executing stock
certificates to execute and issue the necessary certificates for shares of
Common Stock upon the exercise of this Warrant.

     8. Notices. In case:

          (a) the Company shall take a record of the holders of its Common Stock
(or other stock or securities at the time receivable upon the exercise of this
Warrant) for the purpose of entitling them to receive any dividend or other
distribution, or any right to subscribe for or purchase any shares of stock of
any class or any other securities, or to receive any other right, or

                                      -6-

<PAGE>

          (b) of any capital reorganization of the Company, any reclassification
of the capital stock of the Company, any consolidation or merger of the Company
with or into another corporation, or any conveyance of all or substantially all
of the assets of the Company to another corporation, or

          (c) of any voluntary dissolution, liquidation of winding-up of the
Company, then, and in each such case, the Company will mail or cause to be
mailed to the Holder or Holders a notice specifying, as the case may be, (A) the
date on which a record is to be taken for the purpose of such dividend,
distribution or right, and stating the amount and character of such dividend,
distribution or right, or (B) the date on which such reorganization,
reclassification, consolidation, merger, conveyance, dissolution, liquidation or
winding-up is to take place, and the time, if any is to be fixed, as of which
the holders of record of Common Stock (or such stock or securities at the time
receivable upon the exercise of this Warrant) shall be entitled to exchange
their shares of Common Stock (or such other stock or securities) for securities
or other property deliverable upon such reorganization, reclassification,
consolidation, merger, conveyance, dissolution, liquidation or winding-up. Such
notice shall be mailed at least fifteen (15) days prior to the date therein
specified.

     9. Rights of Shareholders. The Holder shall not be entitled to vote or
receive dividends or be deemed the holder of Common Stock or any other
securities of the Company that may at any time be issuable on the exercise
hereof for any purpose, nor shall anything contained herein be construed to
confer upon the Holder, as such, any of the rights of a shareholder of the
Company or any right to vote for the election of directors or upon any matter
submitted to shareholders at any meeting thereof, or to give or withhold consent
to any corporate action (whether upon any recapitalization, issuance of stock,
reclassification of stock, change of par value, or change of stock to no par
value, consolidation, merger, conveyance, or otherwise) or to receive notice of
meetings, or to receive dividends or subscription rights or otherwise until the
Warrant shall have been exercised and the shares of Common Stock purchasable
upon the exercise hereof shall have been issued, as provided herein.

     10. Fractional Shares. No fractional shares will be issued in connection
with any exercise hereunder, but in lieu of such fractional shares the Company
will make a cash payment therefor upon the basis of the Exercise Price then in
effect.

     11. Assignment. This Warrant applies to, inures to the benefit of, and
binds the successors and assigns of the parties hereto. Any transfer of this
Warrant will be effected only by surrender of this Warrant to the Company and
reissuance of a new note to transferee. The Holder and any subsequent holder(s)
of this Warrant receive this Warrant subject to the foregoing items and
conditions, and agree to comply with the foregoing terms and conditions for the
benefit of the Company and any other holders.

     12. Notices. Any notice, request or other communication required or
permitted hereunder shall be in writing and shall be deemed to have been duly
given (i) when received, if personally delivered, faxed, sent by nationally
recognized courier or U.S. Mail return-receipt requested, or (ii) on the third
(3rd) business day after deposit in the U.S. Mail, if sent by first-class mail,
in any such case to the address of the Holder set forth below and to the Company
at Alsius Corporation, 15570 Laguna Canyon Road, Suite 150, Irvine, California
92618, fax

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(949) 753-1819, Attention: President. Any party hereto may by notice so given
change its address for future notice hereunder.

     13. Warrant Register. This Warrant is transferable only upon the books of
the Company which it shall cause to be maintained for such purpose. The Company
may treat the registered holder of this Warrant as he, she or it appears on the
Company's books at any time as the Holder for all purposes.

     14. Amendment, Waiver, Etc. The terms of this Warrant may be amended or
waived only upon the written agreement of the Company and the Holder; provided,
however, that during the time (and only during the time) the Bridge Notes are
outstanding, the terms of this Warrant and all of the other Warrants issued by
the Company in connection with the Bridge Notes may be amended or waived upon
the written agreement of the Company and the holders of a majority or more of
the aggregate principal amount of all Bridge Notes (the "Majority Holders"),
whether or not the Holder of this Warrant agrees thereto, as long as such
amendment or waiver is the same for all Warrants. Any such amendment or waiver
agreed to by the Company and the Majority Holders during the time the Bridge
Notes are outstanding will be binding on the holders of all Warrants. Amendments
or waivers to which the Company and the Majority Holders may agree, and which
will be binding on holders of all Warrants, include, but are not limited to, (i)
shortening the term of the Warrants, (ii) changing the exercise price of the
Warrants, or (iii) reducing the number of shares for which the Warrants are
exercisable (as long as such reduction is proportionally the same for each
Warrant holder based on the shares covered by such holder's Warrant relative to
the shares covered by all Warrants).

     15. Heading; References. All headings used herein are used for convenience
only and shall not be used to construe or interpret this Warrant. Except where
otherwise indicated, all references herein to Sections refer to Sections hereof.

     16. Severability. If any provision or set of provisions of this Warrant (or
any portion thereof) is held by an arbitrator or court of competent jurisdiction
to be invalid, illegal or unenforceable for any reason whatever: (a) such
provision shall be limited or modified in its application to the minimum extent
necessary to avoid the invalidity, illegality or unenforceability of such
provision and such modified provision shall be reduced to a writing and signed
by the parties hereto; (b) the validity, legality and enforceability of the
remaining provisions of this Warrant shall not in any way be affected or
impaired thereby; and (c) to the fullest extent possible, the provisions of this
Warrant shall be construed so as to give effect to the intent manifested by the
provision (or portion thereof) held invalid, illegal or unenforceable.

     17. Effect of Amendment or Waiver. Each Holder acknowledges that by the
operation of Section 14 hereof, less than all of the Holders of Warrants (or
such transferees of Warrants) may effect an amendment or waiver of provisions of
the Warrants and may therefore diminish or eliminate all rights of such Holder
under this Warrant even though such Holder has not consented to the amendment or
waiver.

     18. Governing Law. This Warrant shall be governed by and construed in
accordance with the laws of the State of California, without regards to its
conflict of laws provisions.

                                      -8-

<PAGE>

     IN WITNESS WHEREOF, the undersigned have caused this Warrant to be executed
by the undersigned as of the date first set forth above.

                                        ALSIUS CORPORATION

                                        By:
                                            ------------------------------------
                                            William Worthen
                                            President & CEO

                                        HOLDER:

                                        By:
                                            ------------------------------------
                                        Name:
                                              ----------------------------------
                                        Title:
                                               ---------------------------------
                                        Address:
                                                 -------------------------------

                                                 -------------------------------

                                                 -------------------------------
                                        Fax:
                                             -----------------------------------
                                        Phone:
                                               ---------------------------------

                                      -9-

<PAGE>

                                     ANNEX I
                                   TO WARRANT

                        Stock Warrant Notice of Exercise

Ladies/Gentlemen:

On this date the undersigned, ______________________________, hereby acquires
from Alsius Corporation, a California corporation (the "Company"), an aggregate
of _____________ shares of Common Stock, as defined in the Warrant which is
exercised hereby (the "Restricted Securities").

1. Investment Intent. The undersigned represents and warrants that:

     (a) The Restricted Securities have been acquired by the undersigned for
investment and not with a view to the sale or other distribution thereof within
the meaning of the Securities Act of 1933, as amended (the "1933 Act") and the
undersigned has no present intention of selling or otherwise disposing of all or
any portion of the Restricted Securities.

     (b) The undersigned has acquired the Restricted Securities for the
undersigned's own account and no one else has any beneficial ownership in the
Restricted Securities.

2. Restrictions on Transfer. The undersigned understands that:

     (a) In reliance upon the representations and warranties set forth herein,
the Restricted Securities have not been registered with the Securities and
Exchange Commission (the "SEC"), and accordingly may not be offered, sold or
otherwise transferred except in compliance with the 1933 Act (including any
exemptions from registration thereunder);

     (b) The undersigned must bear the economic risk of the undersigned's
investment in the Restricted Securities indefinitely unless and until the
Restricted Securities are registered pursuant to the 1933 Act or, in the opinion
of counsel in form and substance satisfactory to the Company, an exemption from
the registration requirement is available;

     (c) The undersigned cannot be assured that any exemption from the
registration requirement will be available should the undersigned desire to
transfer the Restricted Securities, and, therefore, the undersigned may not be
able to dispose of or otherwise transfer the Restricted Securities, under the
circumstances, in the amounts, or at the time proposed by the undersigned; and

     (d) Rule 144 promulgated under the 1933 Act, which provides for certain
limited, routine sales of unregistered securities, is not presently available
with respect to the Restricted Securities, and the Company is under no
obligation to furnish the information that might be necessary to enable the
undersigned to sell any of the Restricted Securities under Rule 144.

3. Legend and Stop-Transfer Orders. The undersigned understands that, if
required by applicable federal securities laws at the date of issuance of the
Restricted Securities, certifies or other instruments representing any of the
Restricted Securities acquired by the undersigned will

<PAGE>

bear a legend substantially similar to the following, in addition to any other
legends required by federal or state laws, or by any contractual agreement
binding upon the undersigned with respect to the Restricted Securities:

     THE SECURITIES EVIDENCED HEREBY HAVE NOT BEEN REGISTERED OR QUALIFIED UNDER
     THE SECURITIES ACT OF 1933, AS AMENDED, OR THE SECURITIES LAWS OF ANY
     STATE, AND MAY BE OFFERED, SOLD, PLEDGED OR HYPOTHECATED ONLY IF REGISTERED
     AND QUALIFIED PURSUANT TO THE RELEVANT PROVISIONS OF FEDERAL AND STATE
     SECURITIES LAWS OR IF THE COMPANY IS PROVIDED AN OPINION OF COUNSEL
     REASONABLY SATISFACTORY TO THE COMPANY THAT REGISTRATION AND QUALIFICATION
     UNDER FEDERAL AND STATE SECURITIES LAWS IS NOT REQUIRED OR IF THE COMPANY
     OTHERWISE SATISFIES ITSELF THAT REGISTRATION IS NOT REQUIRED.

     The undersigned agrees that, to ensure and enforce compliance with the
restrictions imposed by applicable law and those referred to in the foregoing
legend, or elsewhere herein, the Company may issue appropriate "stop transfer
instructions to its transfer agent, if any, with respect to any certificate or
other instrument representing Restricted Securities, or if the Company transfers
its own securities, that it may make appropriate notation to the same effect in
the Company's records.

     Notwithstanding the legend above, no registration statement or opinion of
counsel shall be necessary for any transfer of Restricted Securities: (i) in
compliance with Rule 144 or Rule 144A of the 1933 Act, (ii) by gift, will or
intestate succession by the Holder to his or her spouse or lineal descendants or
ancestors or any trust for any of the foregoing or (iii) pursuant to a transfer
to any partner, former partner, affiliate or the estate of any such partner of
the Holder; provided that, in each of the foregoing cases, the transferee agrees
in writing to be subject to the terms of the Warrant.

-------------------------------------
(Printed name if entity)
(Signature of Individual)

(Please fill in and sign below only
if entity):

By:
    ---------------------------------
    (Signature)

Printed name:
              -----------------------
Its:
     --------------------------------
Date:
      -------------------------------

                                      -11-

<PAGE>

                                    ANNEX II
                                   TO WARRANT

                     ASSIGNMENT FORM FOR ALSIUS CORPORATION
                                  STOCK WARRANT

     TO ASSIGN THE FOREGOING WARRANT, EXECUTE THIS FORM AND SUPPLY REQUIRED
INFORMATION. DO NOT USE THIS FORM TO EXERCISE THE WARRANT TO PURCHASE SHARES.

     PLEASE NOTE: THE WARRANT HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT
OF 1933, AS AMENDED, OR UNDER THE APPLICABLE STATE SECURITIES LAWS. THE WARRANT
IS SUBJECT TO RESTRICTIONS ON TRANSFERABILITY AND RESALE AND MAY NOT BE
TRANSFERRED OR RESOLD EXCEPT AS PERMITTED UNDER THE WARRANT.

FOR VALUE RECEIVED, the foregoing Warrant for the purchase of capital stock of
Alsius Corporation and all rights evidenced thereby are hereby assigned to

Name of assignee: ______________________________________________________________

Address of assignee: ___________________________________________________________

                     ___________________________________________________________

Date: _______________________________

Assigning Holder's Name: _______________________________________________________

Assigning Holder's Signature: __________________________________________________

Assigning Holder's Address: ____________________________________________________

                            ____________________________________________________

The name and signature of the assigning Holder must be exactly the same as the
Holder's name appears on the face of the assigned warrant, without alteration or
enlargement or any change whatever. Officers of corporations and those acting in
fiduciary or their representative capacity should file with this Assignment
proper evidence of their authority to so act.<PAGE>

                                                                     Exhibit 4.5

                             PREFERRED STOCK WARRANT

NEITHER THIS WARRANT NOR THE SECURITIES ISSUABLE UPON EXERCISE OF THIS WARRANT
HAVE BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED. NO SALE OR
DISPOSITION MAY BE EFFECTED EXCEPT IN COMPLIANCE WITH RULE 144 UNDER SAID ACT OR
WITHOUT AN EFFECTIVE REGISTRATION STATEMENT RELATED THERETO OR AN OPINION OF
COUNSEL FOR THE HOLDER, SATISFACTORY TO THE COMPANY, THAT SUCH REGISTRATION IS
NOT REQUIRED UNDER THE ACT OR RECEIPT OF A NO-ACTION LETTER FROM THE SECURITIES
AND EXCHANGE COMMISSION.

             WARRANT TO PURCHASE SHARES OF SERIES F PREFERRED STOCK

                                                             Dated: May 31, 2005

THIS CERTIFIES THAT, for value received, Oxford Finance Corporation, ("Holder")
is entitled to subscribe for and purchase that number of shares as set forth in
paragraph 1 below of the fully paid and non-assessable Series F Preferred Stock
(the "Shares" or the "Preferred Stock") of Alsius Corporation, a California
corporation (the "Company"), at the Warrant Price (as hereinafter defined),
subject to the provisions and upon the terms and conditions hereinafter set
forth. As used herein, the term "Series F Preferred Stock" shall mean the
Company's presently authorized Series F Preferred Stock, and any stock into
which such Series F Preferred Stock may hereafter be exchanged.

1. Warrant Price. The Warrant Price shall initially be the lower of (i) Three
Dollars ($3.00) per share and (ii) the lowest effective price per share (on a
common stock equivalent basis and taking into account any securities issued
together with the preferred stock) at which shares of the Company's convertible
preferred stock are sold in the next Qualified Financing; provided, however, if
the Qualified Financing has not closed prior to the exercise of this Warrant,
then the Warrant Price shall be Three Dollars ($3,00) per share. A "Qualified
Financing" shall mean the sale of the convertible preferred stock of the Company
to purchasers which include venture capital investors in an aggregate gross cash
amount not less than $2,000,000 (excluding any bridge debt actually converted
into equity.). The number of shares for which this Warrant is exercisable shall
be the nearest whole number determined by dividing $350,000 by the Warrant Price
determined pursuant to this paragraph

2. Conditions to Exercise. The purchase right represented by this Warrant may be
exercised at any time, or from time to time, in whole or in part during the term
commencing on the date hereof and ending on the earlier of:

     (a)  5:00 P.M. Eastern Standard time on the eighth annual anniversary of
          this Warrant Agreement; or

     (b)  the earlier termination of this Warrant pursuant to Section 3(e).

     In the event that, although the Company shall have given notice of a
transaction pursuant to subparagraph [3(e)] hereof, the transaction does not
close within 60 days of the day specified by the Company, unless otherwise
elected by the Holder any exercise of the Warrant subsequent to the giving of
such notice shall be rescinded and the Warrant shall again be exercisable until
terminated in accordance with this Paragraph 2.

3. Method of Exercise; Payment; Issuance of Shares; Issuance of New Warrant.

     (a)  Cash Exercise. Subject to Section 2 hereof, the purchase right
          represented by this Warrant may be exercised by the Holder hereof, in
          whole or in part, by the surrender of this Warrant (with a duly
          executed Notice of Exercise in the form attached hereto) at the
          principal office of the Company (as set forth in Section 18 below) and
          by payment to the Company, by check, of an amount equal to the then
          applicable Warrant Price per share multiplied by the number of shares
          then being purchased. In the event of any exercise of the rights
          represented by this Warrant, certificates for the shares of stock so
          purchased shall be in the name of, and delivered to, the Holder
          hereof, or as such Holder may direct (subject to the terms of transfer
          contained herein and upon payment by such Holder hereof of any
          applicable transfer taxes). Such delivery shall be made within 10
          business days after exercise of the Warrant and at the Company's
          expense and, unless this Warrant

                                   Page 1 of 9

<PAGE>

                             PREFERRED STOCK WARRANT

          has been fully exercised or expired, a new Warrant having terms and
          conditions substantially identical to this Warrant and representing
          the portion of the Shares, if any, with respect to which this Warrant
          shall not have been exercised, shall also be issued to the Holder
          hereof within 10 business days after exercise of the Warrant.

     (b)  Net Issue Exercise. In lieu of exercising this Warrant pursuant to
          Section 3(a), Holder may elect to receive shares equal to the value of
          this Warrant (or of any portion thereof remaining unexercised) by
          surrender of this Warrant at the principal office of the Company
          together with notice of such election, in which event the Company
          shall issue to Holder the number of shares of the Company's Series ___
          Preferred Stock computed using the following formula:

              Y (A-B)
          X = -------
                 A

          Where X = the number of shares of Series F Preferred Stock to be
          issued to Holder.

          Y = the number of shares of Series F Preferred Stock purchasable under
          this Warrant (at the date of such calculation).

          A = the Fair Market Value of one share of the Company's Series F
          Preferred Stock (at the date of such calculation).

          B = Warrant Exercise Price (as adjusted to the date of such
          calculation).

     (c)  Fair Market Value. For purposes of this Section 3, Fair Market Value
          of one share of the Company's Series F Preferred Stock shall mean:

          (i)  If the Common Stock is traded on NASDAQ or Over-The-Counter or on
               an exchange, the per share Fair Market Value for the Series F
               Preferred Stock will be the average of the closing bid and asked
               prices of the Common Stock quoted in the Over-The-Counter Market
               Summary or the closing price quoted on any exchange on which the
               Common Stock is listed, whichever is applicable, as published in
               the Western Edition of The Wall Street Journal for the ten (10)
               trading days prior to the date of determination of Fair Market
               Value multiplied by the number of shares of Common Stock into
               which each share of Series F Preferred Stock is then convertible;
               or

          (ii) In the event of an exercise in connection with a merger,
               acquisition or other consolidation in which the Company is not
               the surviving entity, the per share Fair Market Value for the
               Series F Preferred Stock shall be the value to be received per
               share of Series F Preferred Stock by all Holders of the Series F
               Preferred Stock in such transaction as determined by the Board of
               Directors; or

          (iii) In any other instance, the per share Fair Market Value for the
               Series F Preferred Stock shall be as determined in good faith by
               the Company's Board of Directors unless Holder elects to have
               such fair market value determined by an appraiser, which election
               must be made by Holder within ten (10) business days of the date
               the Company notifies Holder of the fair market value as
               determined by its Board of Directors. In the event of such an
               appraisal, the cost thereof shall be borne by the Holder unless
               such appraisal results in a fair market value in excess of 115%
               of that determined by the Company's Board of Directors, in which
               event the Company shall bear the cost of such appraisal.

               In the event of 3(c)(ii) or 3(c)(iii), above, the Company's Board
          of Directors shall prepare a certificate, to be signed by an
          authorized Officer of the Company, setting forth in reasonable detail
          the basis for and method of determination of the per share Fair Market
          Value of the Series Preferred Stock. The Board will also certify to
          the Holder that this per share Fair Market Value

                                   Page 2 of 9

<PAGE>

                             PREFERRED STOCK WARRANT

          will be applicable to all holders of the Company's Series F Preferred
          Stock. Such certification must be made to Holder at least fifteen (15)
          business days prior to the proposed effective date of the merger,
          consolidation, sale, or other triggering event as defined in 3(c)(ii)
          and 3(c)(iii).

     (d)  Automatic Exercise. To the extent this Warrant is not previously
          exercised, it shall be automatically exercised in accordance with
          Sections 3(b) and 3(c) hereof (even if not surrendered) immediately
          before its expiration.

     (e)  Treatment of Warrant Upon Acquisition of Company.

          (i)  Upon the written request of the Company, Holder agrees that, in
               the event of an Acquisition (as defined below) in which the sole
               consideration is cash, either (a) Holder shall exercise its
               conversion or purchase right under this Warrant and such exercise
               will be deemed effective immediately prior to the consummation of
               such Acquisition or (b) if Holder elects not to exercise the
               Warrant, this Warrant will expire upon the consummation of such
               Acquisition. The Company shall provide the Holder with written
               notice of its request relating to the foregoing (together with
               such reasonable information as the Holder may request in
               connection with such contemplated Acquisition giving rise to such
               notice), which is to be delivered to Holder not less than ten
               (10) days prior to the closing of the proposed Acquisition.

          (ii) Upon written request of the Company, Holder agrees that, in the
               event of a stock for stock Acquisition of the Company by a
               publicly traded acquirer if, on the record date for the
               Acquisition, the fair market value of the Shares (or other
               securities issuable upon exercise of this Warrant) is equal to or
               greater than four [4] times the Warrant Price, Company may
               require the Warrant to be deemed automatically exercised and the
               Holder shall participate in the Acquisition as a holder of the
               Shares (or other securities issuable upon exercise of the
               Warrant) on the same terms as other holders of the same class of
               securities of the Company.

          (iii) Upon the closing of any Acquisition other than those
               particularly described in subsections (i) or (ii) above, the
               successor entity shall assume the obligations of the Warrant, and
               the Warrant shall be exercisable for the same securities, cash,
               and property as would be payable for the Shares issuable upon
               exercise of the unexercised portion of this Warrant as if such
               Shares were outstanding on the record date for the Acquisition
               and subsequent closing. The Warrant Price and/or number of Shares
               shall be adjusted accordingly.

          (iv) For the purpose of this Warrant, "Acquisition" means any sale,
               license, or other disposition of all or substantially all of the
               assets of the Company, or any reorganization, consolidation, or
               merger of the Company where the holders of the Company's
               securities before the transaction beneficially own less than 50%
               of the outstanding voting securities of the surviving entity
               after the transaction, other than in connection with an initial
               public offering.

4. Representations and Warranties of Holder and Restrictions on Transfer Imposed
by the Securities Act of 1933.

     (a)  Representations and Warranties by Holder. The Holder represents and
          warrants to the Company with respect to this purchase as follows:

          (i)  The Holder has substantial experience in evaluating and investing
               in private placement transactions of securities of companies
               similar to the Company so that the Holder is capable of
               evaluating the merits and risks of its investment in the Company
               and has the capacity to protect its interests.

                                   Page 3 of 9

<PAGE>

                             PREFERRED STOCK WARRANT

          (ii) The Holder is acquiring the Warrant and the Shares of Series F
               Preferred Stock issuable upon exercise of the Warrant and Common
               Stock issuable upon conversion thereof (collectively the
               "Securities") for investment for its own account and not with a
               view to, or for resale in connection with, any distribution
               thereof. The Holder understands that the Securities have not been
               registered under the Securities Act of 1933, as amended (the
               "Act") by reason of a specific exemption from the registration
               provisions of the Act, which depends upon, among other things,
               the bona fide nature of the investment intent as expressed
               herein. In this connection, the Holder understands that, in the
               view of the Securities and Exchange Commission (the "SEC"), the
               statutory basis for such exemption may be unavailable if this
               representation was predicated solely upon a present intention to
               hold the Securities for the minimum capital gains period
               specified under tax statutes, for a deferred sale, for or until
               an increase or decrease in the market price of the Securities or
               for a period of one year or any other fixed period in the future.

          (iii) The Holder acknowledges that the Securities must be held
               indefinitely unless subsequently registered under the Act or an
               exemption from such registration is available. The Holder is
               aware of the provisions of Rule 144 promulgated under the Act
               ("Rule 144") which permits limited resale of securities purchased
               in a private placement subject to the satisfaction of certain
               conditions, including, in case the securities have been held for
               more than one but less than two years, the existence of a public
               market for the shares, the availability of certain public
               information about the Company, the resale occurring not less than
               one year after a party has purchased and paid for the security to
               be sold, the sale being through a "broker's transaction" or in a
               transaction directly with a "market maker" (as provided by Rule
               144(f)) and the number of shares or other securities being sold
               during any three-month period not exceeding specified
               limitations.

          (iv) The Holder further understands that at the time the Holder wishes
               to sell the Securities there may be no public market upon which
               such a sale may be effected, and that even if such a public
               market exists, the Company may not be satisfying the current
               public information requirements of Rule 144, and that in such
               event, the Holder may be precluded from selling the Securities
               under Rule 144 unless a) a one-year minimum holding period has
               been satisfied and b) the Holder was not at the time of the sale
               nor at any time during the three-month period prior to such sale
               an affiliate of the Company.

          (v)  The Holder has had an opportunity to discuss the Company's
               business, management and financial affairs with its management
               and an opportunity to review the Company's facilities. The Holder
               understands that such discussions, as well as the written
               information issued by the Company, were intended to describe the
               aspects of the Company's business and prospects which it believes
               to be material but were not necessarily a thorough or exhaustive
               description.

          (vi) The Holder is an "accredited investor," as such term is defined
               in Rule 501(a) promulgated under the Act.

     (b)  Legends. Each certificate representing the Securities shall be
          endorsed with the following legend:

          THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF
          1933, AS AMENDED, AND MAY NOT BE TRANSFERRED UNLESS COVERED BY AN
          EFFECTIVE REGISTRATION STATEMENT UNDER SAID ACT, A "NO ACTION" LETTER
          FROM THE SECURITIES AND EXCHANGE COMMISSION WITH RESPECT TO SUCH
          TRANSFER, A TRANSFER MEETING THE REQUIREMENTS OF RULE 144 OF THE
          SECURITIES AND EXCHANGE COMMISSION, OR (IF REASONABLY REQUIRED BY THE
          COMPANY) AN OPINION OF COUNSEL SATISFACTORY TO THE ISSUER TO THE
          EFFECT THAT ANY SUCH TRANSFER IS EXEMPT FROM SUCH REGISTRATION.

                                   Page 4 of 9

<PAGE>

                             PREFERRED STOCK WARRANT

          The Company need not enter into its stock register a transfer of
          Securities unless the conditions specified in the foregoing legend are
          satisfied. The Company may also instruct its transfer agent not to
          register the transfer of any of the Shares unless the conditions
          specified in the foregoing legend are satisfied.

     (c)  Removal of Legend and Transfer Restrictions. The legend relating to
          the Act endorsed on a certificate pursuant to paragraph 4(b) of this
          Warrant and the stop transfer instructions with respect to the
          Securities represented by such certificate shall be removed and the
          Company shall issue a certificate without such legend to the Holder of
          the Securities if (i) the Securities are registered under the Act and
          a prospectus meeting the requirements of Section 10 of the Act is
          available or (ii) the Holder provides to the Company an opinion of
          counsel for the Holder reasonably satisfactory to the Company, or a
          no-action letter or interpretive opinion of the staff of the SEC
          reasonably satisfactory to the Company, to the effect that public
          sale, transfer or assignment of the Securities may be made without
          registration and without compliance with any restriction such as Rule
          144.

5. Condition of Transfer or Exercise of Warrant. It shall be a condition to any
transfer or exercise of this Warrant that at the time of such transfer or
exercise, the Holder shall provide the Company with a representation in writing
that the Holder or transferee is acquiring this Warrant and the shares of Series
F Preferred Stock to be issued upon exercise, for investment purposes only and
not with a view to any sale or distribution,, or will provide the Company with a
statement of pertinent facts covering any proposed distribution and a written
agreement that such Holder or transferee agrees to be bound by the provisions of
this Warrant. As a further condition to any transfer of this Warrant or any or
all of the shares of Series F Preferred Stock issuable upon exercise of this
Warrant, other than a transfer registered under the Act, the Company must have
received a legal opinion, in form and substance satisfactory to the Company and
its counsel, reciting the pertinent circumstances surrounding the proposed
transfer and stating that such transfer is exempt from the registration and
prospectus delivery requirements of the Act. Each certificate evidencing the
shares issued upon exercise of the Warrant or upon any transfer of the shares
(other than a transfer registered under the Act or any subsequent transfer of
shares so registered) shall, at the Company's option, contain a legend in form
and substance satisfactory to the Company and its counsel, restricting the
transfer of the shares to sales or other dispositions exempt from the
requirements of the Act.

     As further condition to each transfer, the Holder shall surrender this
Warrant to the Company and the transferee shall receive and accept a Warrant, of
like tenor and date, executed by the Company.

6. Stock Fully Paid; Reservation of Shares. All Shares which may be issued upon
the exercise of the rights represented by this Warrant will, upon issuance, be
fully paid and non-assessable, and free from all taxes, liens, and charges with
respect to the issue thereof. During the period within which the rights
represented by this Warrant may be exercised, the Company will at all times have
authorized, and reserved for issuance upon exercise of the purchase rights
evidenced by this Warrant, a sufficient number of shares of its Series F
Preferred Stock to provide for the exercise of the rights represented by this
Warrant.

7. (a) Adjustment for Certain Events. In the event of changes in the outstanding
Series F Preferred Stock by reason of stock dividends, split-ups,
recapitalizations, reclassifications, mergers, consolidations, combinations or
exchanges of shares, separations, reorganizations, liquidations, or the like,
the number and class of shares available under the Warrant in the aggregate and
the Warrant Price shall be correspondingly adjusted, as appropriate, by the
Board of Directors of the Company. The adjustment shall be such as will give the
Holder of this Warrant upon exercise for the same aggregate Warrant Price the
total number, class and kind of shares as it would have owned had the Warrant
been exercised prior to the event and had it continued to hold such shares until
after the event requiring adjustment.

     (b) Other Anti-dilution Protections. Additional anti-dilution rights
applicable to the Series F Preferred Stock purchasable hereunder are as set
forth in the Certificate of Incorporation. Such anti-dilution rights shall not
be restated, amended, modified or waived in any manner that is adverse to the
Holder hereof and different from other holders of Series F Preferred Stock
without the Holder's written consent. The Company shall promptly provide the
Holder with any restatement, amendment, modification or waiver of the
Certification of Incorporation.

                                   Page 5 of 9

<PAGE>

                             PREFERRED STOCK WARRANT

8. Notice of Adjustments. Whenever any Warrant Price shall be adjusted pursuant
to Section 7 hereof, the Company shall prepare a certificate signed by its
president or chief financial officer setting forth, in reasonable detail, the
event requiring the adjustment, the amount of the adjustment, the method by
which such adjustment was calculated, and the Warrant Price and number of shares
issuable upon exercise of the Warrant after giving effect to such adjustment,
and shall cause copies of such certificate to be mailed (by certified or
registered mail, return receipt required, postage prepaid) within thirty (30)
days of such adjustment to the Holder of this Warrant as set forth in Section 19
hereof.

9. "Market Stand-Off" Agreement. Holder hereby agrees that for a period of up to
180 days following the effective date of the first registration statement of the
Company covering common stock (or other securities) to be sold on its behalf of
the Company in an underwritten public offering, it will not, to the extent
requested by the Company and any underwriter, sell or otherwise transfer or
dispose of (other than to designees or transferees who agree to be similarly
bound) any of the Shares at any time during such period except common stock
included in such registration; provided, however, that all officers and
directors of the Company who hold securities of the Company or all other persons
who own at least one percent (1%) of the Company's outstanding voting equity
securities enter into similar agreements.

10. Transferability of Warrant. This Warrant is transferable on the books of the
Company at its principal office by the registered Holder hereof upon surrender
of this Warrant properly endorsed, subject to compliance with Section 5 and
applicable federal and state securities laws. The Company shall issue and
deliver to the transferee a new Warrant representing the Warrant so transferred.
Upon any partial transfer, the Company will issue and deliver to Holder a new
Warrant with respect to the Warrant not so transferred. Holder shall not have
any right to transfer any portion of this Warrant to any direct competitor of
the Company.

11. Registration Rights. The Holder shall have piggyback registration rights.

12. No Fractional Shares. No fractional share of Series F Preferred Stock will
be issued in connection with any exercise hereunder, but in lieu of such
fractional share the Company shall make a cash payment therefor upon the basis
of the Warrant Price then in effect.

13. Charges, Taxes and Expenses. Issuance of certificates for shares of Series F
Preferred Stock upon the exercise of this Warrant shall be made without charge
to the Holder for any United States or state of the United States documentary
stamp tax or other incidental expense with respect to the issuance of such
certificate, all of which taxes and expenses shall be paid by the Company, and
such certificates shall be issued in the name of the Holder.

14. No Shareholder Rights Until Exercise. This Warrant does not entitle the
Holder hereof to any voting rights or other rights as a shareholder of the
Company prior to the exercise hereof.

15. Registry of Warrant. The Company shall maintain a registry showing the name
and address of the registered Holder of this Warrant. This Warrant may be
surrendered for exchange or exercise, in accordance with its terms, at such
office or agency of the Company, and the Company and Holder shall be entitled to
rely in all respects, prior to written notice to the contrary, upon such
registry.

16. Loss, Theft, Destruction or Mutilation of Warrant. Upon receipt by the
Company of evidence reasonably satisfactory to it of the loss, theft,
destruction or mutilation of this Warrant, and, in the case of loss, theft, or
destruction, of indemnity reasonably satisfactory to it, and, if mutilated, upon
surrender and cancellation of this Warrant, the Company will execute and deliver
a new Warrant, having terms and conditions substantially identical to this
Warrant, in lieu hereof.

17. Miscellaneous.

     (a)  Issue Date. The provisions of this Warrant shall be construed and
          shall be given effect in all respect as if it had been issued and
          delivered by the Company on the date hereof.

                                   Page 6 of 9

<PAGE>

                             PREFERRED STOCK WARRANT

     (b)  Successors. This Warrant shall be binding upon any successors or
          assigns of the Company.

     (c)  Governing Law. This Warrant shall be governed by and construed in
          accordance with the laws of the Commonwealth of Virginia.

     (d)  Headings. The headings used in this Warrant are used for convenience
          only and are not to be considered in construing or interpreting this
          Warrant.

     (e)  Saturdays, Sundays, Holidays. If the last or appointed day for the
          taking of any action or the expiration of any right required or
          granted herein shall be a Saturday or a Sunday or shall be a legal
          holiday in the Commonwealth of Virginia., then such action may be
          taken or such right may be exercised on the next succeeding day not a
          legal holiday.

18. No Impairment. The Company shall not by any action including, without
limitation, amending its Sections or articles of incorporation or by-laws, any
reorganization, transfer of assets, consolidation, merger, share exchange
dissolution, issue or sale of securities or any other voluntary action, avoid or
seek to avoid the observance or performance of any of the terms of the Warrants
or impair the ability of the Holder(s) to realize upon the intended economic
value hereof, but will at all times in good faith assist in the carrying out of
all such terms and in the taking of all such action as may be necessary or
appropriate to protect the rights of the Holder(s) hereof against impairment.
Without limiting the generality of the foregoing, the Company will (a) not
increase the par value of any shares of Series F Preferred Stock issuable upon
the exercise of the Warrants above the amount payable therefor upon such
exercise, (b) take all such action as may be necessary or appropriate in order
that the Company may validly issue fully paid and non-assessable shares of
Series F Preferred Stock upon the exercise of the Warrants, (c) obtain all such
authorizations, exemptions or consents from any public regulatory body having
jurisdiction thereof as may be necessary to enable the Company to perform its
obligations under the Warrants and (d) not reclassify or convert common stock
and (f) not take or permit to be taken any action which would have the effect of
shortening the period provided herein for exercise of the Warrants.

19. Addresses. Any notice required or permitted hereunder shall be in writing
and shall be mailed by overnight courier, registered or certified mail, return
receipt required, and postage pre-paid, or otherwise delivered by hand or by
messenger, addressed as set forth below, or at such other address as the Company
or the Holder hereof shall have furnished to the other party.

          If to the Company: Alsius Corporation
                             15770 Laguna Canyon Road, Suite 150
                             Irvine, California 92618
                             Attn: President

                             With a copy to:
                             Pillsbury Winthrop Shaw Pittman LLP
                             650 Town Center Drive, 7th Floor
                             Costa Mesa, California 92626
                             Attn: Ethan D. Feffer, Esq.

          If to the Holder:  Oxford Finance Corporation
                             133 N. Fairfax Street
                             Alexandria, VA 22314
                             Attn: Chief Financial Officer

IN WITNESS WHEREOF,Alsius Corporation has caused this Warrant to be executed by
its officers thereunto duly authorized.

Dated as of May 31, 2005.

                                   Page 7 of 9

<PAGE>

                             PREFERRED STOCK WARRANT

                          [SIGNATURE APPEARS ON PAGE 8]

ALSIUS CORPORATION

By: /s/ William Worthen
    ---------------------------------
Name: William Worthen
      -------------------------------
Title: President & CEO
       ------------------------------

                                   Page 8 of 9

<PAGE>

                             PREFERRED STOCK WARRANT

                               NOTICE OF EXERCISE

          TO: Alsius Corporatin
              15770 Laguna Canyon Road, Suite 150
              Irvine, California 92618
              Attn: President

1. The undersigned Warrantholder ("Holder") elects to acquire shares of the
Series F Preferred Stock (the "Preferred Stock") of Alsius Corporation, (the
"Company"), pursuant to the terms of the Stock Purchase Warrant dated May 31,
2005, (the "Warrant").

2. The Holder exercises its rights under the Warrant as set forth below:

          ( )  The Holder elects to purchase _____ shares of Series F Preferred
               Stock as provided in Section 3(a), (c) and tenders herewith a
               check in the amount of $_____ as payment of the purchase price.

          ( ) The Holder elects to convert the purchase rights into shares of
               Series F Preferred Stock as provided in Section 3(b) of the
               Warrant.

3. The Holder surrenders the Warrant with this Notice of Exercise.

4. The Holder represents that it is acquiring the aforesaid shares of Series F
Preferred Stock for investment and not with a view to, or for resale in
connection with, distribution and that the Holder has no present intention of
distributing or reselling the shares.

     Holder acknowledges and agrees to be bound by the provisions of the
Warrant, including, without limitation, the Market Stand-off Agreement contained
therein.

5. Please issue a certificate representing the shares of the Series F Preferred
Stock in the name of the Holder or in such other name as is specified below:

Name:
      -------------------------------
Address:
         ----------------------------
Taxpayer I.D.:
               ----------------------

Oxford Finance Corporation

By:
    ---------------------------------
Name:
      -------------------------------
Title:
       ------------------------------
Date:
      -------------------------------

                                   Page 9 of 9

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