<PAGE>   1
                                                                    EXHIBIT 4.12
                      AMERICAN RESIDENTIAL SERVICES, INC.
                 CONVERTIBLE SENIOR SUBORDINATED NOTES, SERIES A

No. ________                                                       $___________


ORIGINAL ISSUE DATE:                              INTEREST RATE: %

INITIAL CONVERSION PRICE:                      CONVERTIBILITY COMMENCEMENT DATE:
                             INITIAL TARGET VALUE:

REDEMPTION PRICES: If redeemed during 12-month period beginning April 15 in the
year indicated (April 20, in the case of 2000), the redemption price will be:
2000 -- ____%; 2001 -- ____%, 2002 -- ____%, and 2003 -- ____%.

         American Residential Services, Inc., a corporation duly organized and
existing under the laws of the State of Delaware (herein called the "Company,"
which term includes any successor Person under the Indenture hereinafter
referred to), for value received, hereby promises to pay to
__________________________, or registered assigns, the principal sum of
________________ Dollars on April 15, 2004, and to pay interest thereon from the
Original Issue Date shown above or from and including the most recent Interest
Payment Date to which interest has been paid or duly provided for, semi-annually
on April 15 and October 15 in each year, commencing April 15, 1998 at the rate
per annum shown above, until the principal hereof is paid or made available for
payment. The interest so payable, and punctually paid or duly provided for, on
any Interest Payment Date will, as provided in that Indenture, be paid to the
Person in whose name this Note (or one or more Predecessor Securities) is
registered at the close of business on the Regular Record Date for such
interest, which shall be the March 31 or September 30 (whether or not a Business
Day), as the case may be, next preceding that Interest Payment Date. Any such
interest not so punctually paid or duly provided for will forthwith cease to be
payable to the Holder on that Regular Record Date and may either be paid to the
Person in whose name this Note (or one or more Predecessor Securities) is
registered at the close of business on a Special Record Date for the payment of
that Defaulted Interest to be fixed by the Trustee or be paid at any time in any
other lawful manner not inconsistent with the requirements of any securities
exchange on which the Notes may be listed and on such notice as may be required
by that exchange, all as more fully provided in the Indenture. Notice of a
Special Record Date will be given to Holders of Notes not less than 10 days
prior to that Special Record Date. Payment of the principal of and premium, if
any, and interest on this Note will be made at the office or agency of the
Company maintained for that purpose pursuant to Section 10.02 of the Indenture,
in each case in such coin or currency of the United States of America as of the
time of payment is legal tender for payment of public and private debts;
provided, however, that at the option of the Company payment of interest in
respect of the Notes may be made by check mailed to the address of the Person
entitled thereto as such address shall appear in the Security Register for the
Notes.

         REFERENCE IS HEREBY MADE TO THE FURTHER PROVISIONS OF THIS NOTE SET
FORTH ON THE REVERSE HEREOF, WHICH FURTHER PROVISIONS WILL FOR ALL PURPOSES
HAVE THE SAME EFFECT AS IF SET FORTH AT THIS PLACE.

         Unless the certificate of authentication hereon has been executed by
the Trustee referred to on the reverse hereof by manual signature, this Note
will not be entitled to any benefit under the Indenture or be valid or
obligatory for any purpose.

         IN WITNESS WHEREOF, the Company has caused this instrument to be duly
executed under its corporate seal.

Dated:
      ------------

       TRUSTEE'S CERTIFICATE OF AUTHENTICATION
       This is one of the Securities of the series designated,
       described or provided for in the within-mentioned Indenture.

            U.S. TRUST COMPANY OF TEXAS, N.A., as Trustee

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

 AMERICAN RESIDENTIAL SERVICES, INC.



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


Attest:



------------------------------------
   Name:
   Title:





                [SEE REVERSE SIDE FOR RESTRICTIONS ON TRANSFER]


<PAGE>   2



                       AMERICAN RESIDENTIAL SERVICES, INC.
                 CONVERTIBLE SENIOR SUBORDINATED NOTES, SERIES A


         This Security is one of a duly authorized issue of Securities of the
Company designated as its Convertible Senior Subordinated Notes, Series A
(herein called the "Notes") issued and to be issued in one or more series under
an Indenture, dated as of July 31, 1997 (herein called the "Indenture"), between
the Company and U.S. Trust Company of Texas, N.A., as Trustee (herein called the
"Trustee," which term includes any successor trustee under the Indenture), to
which Indenture and all indentures supplemental thereto reference is hereby made
for a statement of the respective rights, limitations of rights, duties and
immunities thereunder of the Company, the Trustee, the holders of Senior
Indebtedness and the Holders of the Securities and of the terms on which the
Securities are, and are to be, authenticated and delivered. The Notes may be
issued from time to time with different interest rates, Redemption Prices,
Convertibility Commencement Dates and Initial Conversion Prices.

         Subject to and on compliance with the provisions of the Indenture, the
Holder of this Note is entitled, at his option, at any time following the
Convertibility Commencement Date set forth on the face hereof and on or before
the close of business on April 15, 2004 or in case this Note or a portion hereof
is called for redemption, then in respect of this Note or that portion hereof
until and including, but (unless the Company defaults in making the payment due
on redemption) not after, the close of business on the second business day
preceding the Redemption Date, and if, as determined as contemplated by Section
3.01 of the Indenture, the average of the closing sale prices per share of
Common Stock for any 20 consecutive trading days occurring on or after that
Convertibility Commencement Date exceeds the Initial Target Value set forth on
the face hereof, as the same may have been appropriately adjusted pursuant to
the Indenture, the Company will be entitled, at its option at any time
thereafter, to convert this Note (or any portion of the principal amount hereof
which is $1,000 or an integral multiple thereof), at the principal amount
hereof, or of such portion, into fully paid and non-assessable shares
(calculated as to each conversion to the nearest 1/100th of a share) of Common
Stock at a conversion price equal to the principal amount set forth on the face
hereof as the Initial Conversion Price for each share of Common Stock (or at the
current adjusted conversion price if an adjustment has been made as provided in
the Indenture) by surrender of this Note, duly endorsed or assigned to the
Company or in blank, to the Company at its office or agency maintained for that
purpose pursuant to Section 10.02 of the Indenture, accompanied by written
notice to the Company in the form provided in this Note (or such other notice as
is acceptable to the Company) that the Holder hereof elects to convert this
Note, or if less than the entire principal amount hereof is to be converted, the
portion hereof to be converted, and, in case that surrender is made during the
period from the opening of business on any Regular Record Date next preceding
any Interest Payment Date to the close of business on that Interest Payment Date
(unless this Note or the portion thereof being converted has been called for
redemption on a Redemption Date, or is repurchaseable on a Repurchase Date
occurring, in either case, within that period), also accompanied by payment in
New York Clearing House funds or other funds acceptable to the Company of an
amount equal to the interest payable on that Interest Payment Date on the
principal amount of this Note then being converted. Subject to the aforesaid
requirement for payment and, in the case of a conversion after the Regular
Record Date next preceding any Interest Payment Date and on or before that
Interest Payment Date, to the right of the Holder of this Note (or any
Predecessor Security) of record at that Regular Record Date to receive an
installment of interest (with certain exceptions provided in the Indenture), no
payment or adjustment is to be made on conversion on account of any interest
accrued hereon or on account of any dividends on the Common Stock issued on
conversion. No fractional shares or scrip representing fractions of shares will
be issued on conversion, but instead of any fractional share the Company will
pay a cash adjustment as provided in the Indenture. The conversion price is
subject to adjustment as provided in the Indenture. In addition, the Indenture
provides that in case of certain consolidations or mergers to which the Company
is a party or the sale or transfer of the properties and assets substantially as
an entirety of the Company in one transaction or a series of related
transactions, the Indenture will be amended, without the consent of any Holders
of Notes, so that this Note, if then outstanding, will be convertible
thereafter, during the period this Note will be convertible as specified above,
only into the kind and amount of securities, cash and other property receivable
on the consolidation, merger, sale or transfer by a holder of the number of
shares of Common Stock into which this Note might have been converted
immediately prior to that consolidation, merger, sale or transfer (assuming that
holder of Common Stock failed to exercise any rights of election and received
per share the kind and amount received per share by a plurality of non-electing
shares).

         The Notes are subject to redemption on not less than 15 and not more
than 60 days' notice by mail, at any time on or after April 20, 2000, as a whole
or in part, at the election of the Company, at the Redemption Prices set forth
on the face hereof (expressed as percentages of the principal amount), plus
accrued interest to the Redemption Date (subject to the right of Holders of
record on the relevant Regular Record Date to receive interest due on an
Interest Payment Date that is on or prior to the Redemption Date).

         In certain circumstances involving the occurrence of a Repurchase Event
(as defined in the Indenture), the Holder hereof will have the right to require
the Company to repurchase this Note at 100% of the principal amount hereof,
together with accrued interest to the Repurchase Date, but interest installments
on this Note whose Stated Maturity is on or prior to that Repurchase Date will
be payable to the Holder of this Note (or any Predecessor Security of this Note)
of record at the close of business on the relevant Record Dates referred to on
the face hereof, all as provided in the Indenture.

         In the event of redemption or conversion of this Note in part only, a
new Note or Notes for the unredeemed or unconverted portion hereof, which will
bear interest at the same rate, and have the same Redemption Prices,
Convertibility Commencement Date and Initial Conversion Price, as this Note,
will be issued in the name of the Holder hereof on the cancellation hereof.

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


                            Form of Conversion Notice
                            -------------------------

TO AMERICAN RESIDENTIAL SERVICES, INC.

         The undersigned registered owner of this Note hereby irrevocably
exercises the option to convert this Note or the portion hereof (which is $1,000
or a multiple thereof) designated below, into shares of Common Stock in
accordance with the terms of the Indenture referred to in this Note, and directs
that the shares issuable and deliverable on the conversion, together with any
check in payment for a fractional share and any Note representing any
unconverted principal amount hereof, be issued and delivered to the registered
owner hereof unless a different name has been provided below. If this Notice is
being delivered on a date after the close of business on a Regular Record Date
and prior to the close of business on the related Interest Payment Date, this
Notice is accompanied by payment in New York Clearing House funds, or other
funds acceptable to the Company, of an amount equal to the interest payable on
that Interest Payment Date on the principal of this Note to be converted (unless
this Note has been called for redemption). If shares or any portion of this Note
not converted are to be issued in the name of a person other than the
undersigned, the undersigned will pay all transfer taxes payable with respect
thereto. Any amount required to be paid by the undersigned on account of
interest accompanies this Note.

Dated:


                            -------------------------
                            -------------------------
                                    Signature(s)

Signature(s) must be guaranteed by a commercial bank or trust company or a
member firm of a national stock exchange if shares of Common Stock are to be
delivered, or Notes to be issued, other than to and in the name of the
registered owner.

--------------------------------
      Signature Guarantee


Fill in for registration of shares of Common Stock if they are to be delivered,
or Notes if they are to be issued, other than to and in the name of the
registered owner: (Please print name and address)

                              Register:                Common Stock
-----------------------------          ---------------
(Name)                                                 Securities
                                       ---------------

                                                  (Check appropriate line(2))
-------------------------------------------------
(Street Address)

-------------------------------------------------
(City, State and zip code)

Principal amount to be converted (if less than all):    $              ,000
                                                         -------------

-------------------------------------------------
Social Security or other Taxpayer Identification Number of owner


The following abbreviations, when used in the inscription on the face of this
certificate, shall be construed as through they were written out in full
according to applicable laws or regulations (additional abbreviations may also
be used though not in the following list):

TEN COM -- as tenants in common
TEN ENT -- as tenants by the entities
JT TEN -- as joint tenants with right of
          survivorship and not as tenants in common

 UNIF GIFT MIN ACT-- __________ Custodian _____________
                       (Cust)                (Minor)

 Under Uniform Gifts to Minors Act ____________
                                     (State)

UNIF TRF MIN ACT --  __________  Custodian until age___
                      (Cust)
                     __________ Under Uniform Transfer
                     (Minor)
                     to Minors Act _________________
                                       (State)



         The indebtedness evidenced by this Note is, in all respects,
subordinate and subject in right of payment to the prior payment in full of all
Senior Indebtedness (as defined in Article I of the Indenture), and this Note is
issued subject to the provisions of the Indenture with respect thereto. Each
Holder of this Note, by accepting the same, (a) agrees to and shall be bound by
those provisions, (b) authorizes and directs the Trustee on his behalf to take
such action as may be necessary or appropriate to effectuate the subordination
so provided and (c) appoints the Trustee his attorney-in-fact for any and all
such purposes.

         If an Event of Default with respect to the Notes occurs and is
continuing, the principal of all the Notes may be declared due and payable in
the manner and with the effect provided in the Indenture.

         The Indenture provides that no Holder of any Note may enforce any
remedy under the Indenture except in the case of failure of the Trustee to act
after notice of default and after request of the Holders of 25% in principal
amount of Outstanding Notes and the offer to the Trustee of indemnity
satisfactory to it; provided, however, that this provision will not prevent the
Holder hereof from enforcing payment of the principal of and premium, if any,
and interest on this Note after the same shall have become due.

         The Indenture permits, with certain exceptions as therein provided, the
amendment thereof and the modification of the rights and obligations of the
Company and the rights of the Holders of the Securities of each series to be
affected under the Indenture at any time by the Company and the Trustee with the
consent of the Holders of not less than a majority in aggregate principal amount
of the Securities at the time Outstanding of all series to be affected, and,
under certain circumstances, by the Company and the Trustee without the consent
of the Holders of Securities of any series to be affected under the Indenture.
The Indenture also contains provisions permitting the Holders of specified
percentages in aggregate principal amount of the Securities at the time
Outstanding of any such series, on behalf of the Holders of all those
Securities, to waive compliance by the Company with certain provisions of the
Indenture and certain past defaults under the Indenture and their consequences.
Any such consent or waiver by the Holder of this Note will be conclusive and
binding on such Holder and on all future Holders of this Note and of any Note
issued on the registration of transfer hereof or in exchange herefor or in lieu
hereof, whether or not notation of that consent or waiver is made upon this
Note.

         No reference herein to the Indenture and no provision of this Note or
of the Indenture will alter or impair the obligation of the Company, which is
absolute and unconditional, to pay the principal of and premium, if any, and
interest on this Note at the times, place and rate, and in the coin or currency,
herein prescribed or to convert this Note as provided in the Indenture.

         As provided in the Indenture and subject to certain limitations therein
set forth, and except as otherwise restricted by a legend printed or otherwise
affixed upon the face hereof, the transfer of this Note is registrable in the
Security Register for the Notes, on surrender of this Note for registration of
transfer at the office or agency of the Company in any place where the principal
of and any premium and interest on this Note are payable, duly endorsed by, or
accompanied by a written instrument of transfer in form satisfactory to the
Company and the Security Registrar for the Notes duly executed by, the Holder
hereof or his attorney duly authorized in writing, and thereon one or more new
Notes, of authorized denominations and for the same aggregate principal amount,
bearing interest at the same rate, and having the same Redemption Price,
Convertibility Commencement Date and Initial Conversion Price, as this Note,
will be issued to the designated transferee or transferees.

         The Notes are issuable only in fully registered form without coupons in
denominations of $1,000 and any integral multiple thereof. As provided in the
Indenture and subject to certain limitations therein set forth, Notes are
exchangeable for a like aggregate principal amount of Notes of a different
authorized denomination, bearing interest at the same rate, and having the same
Redemption Prices, Convertibility Commencement Date and Initial Conversion
Price, as the Notes for which they are exchanged, as requested by the Holder
surrendering the same.

         No service charge will be made for any such registration of transfer or
exchange except as provided in the Indenture, and the Company may require
payment of a sum sufficient to cover any tax or other governmental charge
payable in connection therewith.

         Prior to due presentment of this Note for registration of transfer, the
Company, the Trustee and any agent of the Company or the Trustee may treat the
Person in whose name this Note is registered as the owner hereof for all
purposes, except as provided in this Note, whether or not this Note be overdue,
and neither the Company, the Trustee nor any such agent will be affected by
notice to the contrary.

         All terms used in this Note which are defined in the Indenture have
the meanings assigned to them in the Indenture. The Company will furnish to any
Holder on written request and without charge a copy of the Indenture.

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


                                 Assignment Form
                                 ---------------

If you the holder want to assign this Note, fill in the form below and have your
signature guaranteed:

I or we assign and transfer this Note
to
  -----------------------------------------------------------------------------
(Insert assignee's social security or tax ID
number)
       ------------------------------------------------------------------------
(Print or type assignee's name, address and zip code) and irrevocably
appoint
       ------------------------------------------------------------------------
agent to transfer this Note on the books of the Company. The agent may
substitute another to act for him.

Date:                       Your signature:
      ---------------------                 ----------------------------------
                                           (Sign exactly as your name appears
                                                on the face of this Note)
Signature Guarantee:
                    -----------------------------------------------------------

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


                       Option of Holder to Elect Purchase

         If you wish to have this Note purchased by the Company pursuant to
Section 14.01 of the Indenture, check the Box: [_]

         If you wish to have a portion of this Note (which is $1,000 or an
integral multiple thereof) purchased by the Company pursuant to Section 14.01 of
the Indenture, state the amount you wish to have purchased:
$
 ------------------------------------------------------------------------------
Date:         Your signature:            Tax Identification No.:
      -------                 ---------                          --------------

(Sign exactly as your name appears on the face of this Note)

Signature Guarantee:
                    -----------------------------------------------------------


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


[THE SECURITIES REPRESENTED HEREBY WERE ISSUED IN A TRANSACTION CONSTITUTING A
"BUSINESS COMBINATION" WITHIN THE MEANING OF RULE 145 UNDER THE SECURITIES ACT
OF 1933 TO A PERSON WHO WAS AN "AFFILIATE" OF A PARTY TO THAT TRANSACTION (OTHER
THAN THE ISSUER) PURSUANT TO THE [TITLE OF ACQUISITION AGREEMENT] AMONG THE
ISSUER, [NAME OF COMPANY] AND THE OTHER PERSONS PARTIES THERETO AND MAY NOT BE
SOLD OR OTHERWISE DISPOSED OF WITHOUT COMPLIANCE WITH THE PROVISIONS OF THAT
AGREEMENT AND THE REGISTRATION PROVISIONS OF THE SECURITIES ACT OF 1933 OR AN
APPLICABLE EXEMPTION THEREFROM. A COPY OF THE [TITLE OF ACQUISITION AGREEMENT]
MAY BE OBTAINED FREE OF CHARGE BY CONTACTING THE ISSUER'S GENERAL COUNSEL AT
(713) 599-0100.]