We demonstrate stable microresonator Kerr soliton frequency combs in a III-V platform (AlGaAs on SiO$_2$) through quenching of thermorefractive effects by cryogenic cooling to temperatures between 4~K and 20~K. This cooling reduces the resonators thermorefractive coefficient, whose room-temperature value is an order of magnitude larger than that of other microcomb platforms like Si$_3$N$_4$, SiO$_2$, and AlN, by more than two orders of magnitude, and makes soliton states adiabatically accessible. Realizing such phase-stable soliton operation is critical for applications that fully exploit the ultra-high effective nonlinearity and high optical quality factors exhibited by this platform.
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