Thermoelectricity offers an efficient means of converting heat directly into electricity without greenhouse gas emissions. Recently, the hexagonal γ-GeSe phase and a new class of monolayers called Janus have been synthesized, exhibiting exceptional thermoelectric properties. In this study, we investigate the phonon thermal transport in γ-Ge2SSe Janus monolayers under biaxial strain using density functional theory and Boltzmann transport theory. Our analysis reveals that acoustic phonon modes, particularly the transverse acoustic and longitudinal acoustic modes, dominate the thermal transport. The lattice thermal conductivity (κl) shows a strong dependence on biaxial strain, with a decrease observed under tensile biaxial strain, and the Grüneisen parameter reveals considerable anharmonicity, which promotes phonon scattering and reduces thermal conductivity. At room temperature and at 0% strain, κl of Janus γ-Ge2SSe is measured at 4.41 W/mK, demonstrating moderate thermal transport, while under 2% tensile strain, κl decreases to 3.13 Wm−1 K−1, highlighting the material’s strain sensitivity. These results suggest that strain engineering can be effectively used to optimize the thermoelectric performance of Janus γ-Ge2SSe monolayers, providing valuable insights for energy conversion applications.