<PAGE>

                                 Exhibit 10.6
                                 ------------

              SECOND AMENDMENT TO THE INVESTORS' RIGHTS AGREEMENT

          This Second Amendment to the Investors' Rights Agreement (this
"Amendment") dated as of September 20, 2001, is by and between Amerigon
Incorporated, a California corporation (the "Company"), Big Beaver Investments
LLC, a Delaware limited liability company (the "Lender") and Westar Capital II
LLC, a Delaware limited liability company ("Westar") and amends the Investors'
Rights Agreement dated as of June 8, 1999 among the Company, the Lender and
Westar (as previously amended through the date hereof, the "Investors' Rights
Agreement").  All terms not otherwise defined herein shall have the meanings set
forth in the Investors' Rights Agreement.

                                   RECITALS

          WHEREAS, the Company and the Lender, have entered into a Credit
Agreement (the "2001 Credit Agreement"), dated as of September 20, 2001;

          WHEREAS, the Convertible Promissory Note issued by Company pursuant to
the 2001 Credit Agreement is convertible into Common Stock of the Company as
provided therein;

          WHEREAS, in order to induce the Lender to enter into the 2001 Credit
Agreement, the Company and the Lender have entered into a certain Bridge Loan
Warrant, dated as of September 20, 2001, pursuant to which the Company has
agreed to issue to the Lender certain warrants to purchase shares of Common
Stock of the Company as provided therein;

          WHEREAS, the Investors' Rights Agreement was previously amended by the
parties on March 16, 2000; and

          WHEREAS, the Company desires to amend and restate the definitions of
"Registrable Securities," "Bridge Loan," "Bridge Note," and "Bridge Warrants" in
the Investors' Rights Agreement;

                                   AGREEMENT

          NOW, THEREFORE, in consideration of the foregoing, and for other good
and valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the parties agree to amend the Investors' Rights Agreement as
provided herein:

1.        Section 1.1(g) of the Investors' Rights Agreement is amended and
          restated as follows:

          "The term 'Registrable Securities' means (i) the Common Stock issuable
          or issued upon conversion of the Series A Preferred Stock, (ii) the
          Common Stock issued or issuable upon the exercise of the Bridge Notes
          and the Bridge Warrants, and (iii) any Common Stock of the Company
          issued (or issuable upon the conversion or exercise of any warrant,
          right or other security which is issued) as a dividend or other
          distribution with respect to, or in exchange for or in replacement of
          the shares referenced in (i) and (ii) above,
<PAGE>

     excluding in all cases, however, any Registrable Securities sold by a
     person in a transaction in which his rights under this Section 1 are not
     assigned."

     The following definitions are added after Section 1.1(i) of the Investors'
     Rights Agreement.

     "(j) The term 'Bridge Notes' means the promissory note executed and
     delivered by Company to Big Star Investments LLC ("Big Star") pursuant to a
     Credit Agreement dated as of March 16, 2000 (the "2000 Bridge Credit
     Agreement") and the convertible promissory note executed and delivered by
     the Company to the Lender pursuant to a Credit Agreement dated as of
     September 20, 2001 between Company and the Lender (the "2001 Bridge Credit
     Agreement"), as such agreements may be amended, restated, modified or
     supplemented from time to time.

     (k)  The term 'Bridge Warrants' means a Bridge Loan Warrant dated March 16,
     2000 issued by the Company to Big Star and any additional warrants to
     purchase Common Stock of the Company issued to Big Star pursuant to the
     2000 Bridge Credit Agreement and a Bridge Loan Warrant dated September 20,
     2001 issued by the Company to the Lender and any additional warrants to
     purchase Common Stock of the Company issued to the Lender pursuant to the
     2001 Bridge Credit Agreement."

2.   Right of First Offer.  The Lender and Westar acknowledge that the Company
     --------------------
     has satisfied its obligations to the Major Investors pursuant to Section 2
     of the Investors' Rights Agreement in connection with the issuance of the
     Bridge Notes and the Bridge Warrants.

3.   Miscellaneous.
     -------------

     3.1  Successors and Assigns.  This Amendment and the rights and obligations
          ----------------------
     of the parties hereunder shall inure to the benefit of, and be binding
     upon, their respective successors, assigns and legal representatives.

     3.2  Governing Law.  This Amendment shall be governed by and construed
          -------------
     under the laws of the State of California as applied to agreements among
     California residents entered into and to be performed entirely within
     California.

     3.3  Counterparts.  This Amendment may be executed in two or more
          ------------
     counterparts, each of which shall be deemed an original but all of which,
     when taken together, shall constitute one and the same instrument.

     3.4  Titles and Subtitles.  The titles and subtitles used in this Amendment
          --------------------
     are used for convenience only and are not to be considered in construing or
     interpreting this Amendment.

     3.5  Expenses.  If any action at law or in equity is necessary to enforce
          --------
     or interpret the terms of this Amendment, the prevailing party shall be
     entitled to reasonable attorneys'

                                       2
<PAGE>

     fees, costs and necessary disbursements in addition to any other relief to
     which such party may be entitled.

     3.6  Amendments and Waivers.  Any term of this Amendment may be amended and
          ----------------------
     the observance of any term of this Amendment may be waived (either
     generally or in a particular instance and either retroactively or
     prospectively), only with the written consent of the Company and the
     holders of a majority of the Registrable Securities then outstanding. Any
     amendment or waiver effected in accordance with this paragraph shall be
     binding upon each holder of any Registrable Securities then outstanding,
     each future holder of all such Registrable Securities, and the Company.

     3.7  Severability.  If one or more provisions of this Amendment are held to
          ------------
     be unenforceable under applicable law, such provision shall be excluded
     from this Amendment and the balance of the Amendment shall be interpreted
     as if such provision were so excluded and shall be enforceable in
     accordance with its terms.

     3.8  Entire Agreement; Amendment; Waiver.  This Amendment constitutes the
          -----------------------------------
     entire agreement between the parties hereto with respect to the subject
     matter hereof.
                                       3
<PAGE>

          IN WITNESS WHEREOF, the parties have executed this Amendment as of the
day and year first written above.

                                                  AMERIGON INCORPORATED,
                                                  a California corporation


                                                  By:  /s/ Richard A. Weisbart
                                                     ---------------------------
                                                  Name:  Richard A. Weisbart
                                                  Title: President and Chief
                                                         Executive Officer


                                                  BIG BEAVER INVESTMENTS LLC,
                                                  a Delaware limited liability
                                                  company




                                                  By:  /s/ Paul Oster
                                                     ---------------------------
                                                  Name:  Paul Oster
                                                  Title: Chief Financial Officer


                                                  WESTAR CAPITAL II LLC,
                                                  a Delaware limited liability
                                                  company



                                                  By:  /s/ John Clark
                                                     ---------------------------
                                                  Name:  John Clark
                                                  Title: Managing Partner


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