Aiming at the temperature effect problem of aerospace bevel gears under high-speed and high-load conditions, a time-varying meshing stiffness (TVMS) simulation calculation method is proposed to take into account the influence of temperature. Based on the theory of frictional heat generation, the formula of heat flow density on the tooth surface is deduced, and the relative sliding velocity of the curved bevel gear is simplified by combining with the equivalent cylindrical gear parameters to complete the analysis of tooth contact pressure; the gear pair’s steady-state thermal field is solved via loading the boundary conditions through ANSYS APDL program. The static contact finite element (FE) method is further used to apply the temperature field results as thermal loads, extract the normal contact force and integrated deformation of the meshing tooth surface, and calculate the TVMS. The results show that the increase in temperature leads to thermal expansion in gears, contact regions increases, the integrated deformation decreases, and the TVMS is significantly increased. This work establishes theoretical foundations for thermomechanical coupling design and performance optimization of aerospace bevel gears.