Exhibit 13.1

Certification Pursuant to 18 U.S.C. Section 1350 as Adopted Pursuant to Section 906 of the Sarbanes Oxley Act of 2002

The certification set forth below is being submitted in connection with the Annual Report on Form 20-F for the year ended December 31, 2023 of Cool Company Ltd. (the “Annual Report”) for the purpose of complying with Rule 13a-14(b) or Rule 15d-14(b) of the Securities Exchange Act of 1934 (the “Exchange Act”) and Section 1350 of Chapter 63 of Title 18 of the United States Code.

I, Richard Tyrrell, Chief Executive Officer of Cool Company Ltd., certify that, to the best of my knowledge:

(1) the Annual Report fully complies with the requirements of Section 13(a) or Section 15(d), of the Exchange Act; and

(2) the information contained in the Annual Report fairly presents, in all material respects, the financial condition and results of operations of Cool Company Ltd.

A signed original of this written statement has been provided to the Company and will be retained by the Company and furnished to the SEC or its staff upon request.

Date: March 28, 2024

/s/ Richard Tyrrell

Richard Tyrrell

Chief Executive Officer