Conjugate meshing of involute gears is required in precise gear transmission. However, in the working process, the heat generated in friction results in deformation of the tooth profile of the gear, radial and axial deformation of the shaft and bearing. Meanwhile, there is thermal deformation with non-similarity in the gear box that the shafts and bearings are installed on, which leads to a change of the bearing clearance, axis deflection of the shaft and the gear meshing state. As a result of all these effects, vibration and noise are generated in the transmission system, and it intensifies the possibility of damaging the parts. In this paper, mathematical physics methods and thermal elastic theory are employed to analyze the influence of tooth profiles, gear parameters (transmission ratio i, overlapping coefficients ε, backlash jn, etc), gear meshing, working clearance of the bearing (it relates with the initial clearance, tolerance matching, rotational speed, temperature changes, etc) and the shape of the gear box (cylindricity error, axis deflection, etc) caused by the temperature change. The result can be employed in selecting gear parameters and designing the shape of the gear tooth, bearing clearance and shell structure, and it is also helpful to the design of gear transmissions and screw transmissions.