In this paper, the temperature field, stress field and corresponding thermal distortion of Yb∶YAG crystal slab laser module during high power operation at different cooling temperatures are simulated and analyzed. The results show that the temperature gradient thermal stresses and strains of the slats decrease significantly as the cooling temperature is reduced from 300 K to 77 K. The maximum principal stress is 4.14 MPa, which is only 15.6% of that at room temperature. When the cooling temperature is 77 K, the maximum principal stress is 4.14 MPa, which is only 15.6% of that at room temperature, and the maximum principal strain is 3.82×10^-5, which is only 6% of that at room temperature. In order to analyze the beam quality of the output laser at different cooling temperatures of the Yb∶YAG crystal slab laser module to determine its optimal operating temperature, the 1030 nm probe light passing through the slat in one pass is simulated by the method of light tracing. It can be seen that when the cooling temperature is 77 K, the far-field spot energy is more concentrated, and the PV value of the detection light path difference is 0.7941 μm, which is only 59.6% of that at 300 K. The simulation results show that the low-temperature operation is favourable to the generation of high-power and high-beam-quality laser output from the Yb∶YAG crystal slat laser module, which lays a foundation for the design of high-power and high-beam-quality Yb∶YAG crystal slat lasers.