Aiming at the involute spur gear with logarithmic modification,according to the heat conduction differential equation and the basic equations of thermo-elasticity,the thermal and thermo-elastic fields of involute spur gear at any meshing position are obtained by using the FFT and IFFT programming calculation,the influence of the torque and rotational speed on temperature field and thermal elastic field is discussed.The results show that,the logarithmic modification can reduce the strong thermal at the edges of the gear tooth caused by the edge effect,thus the scuffing resistance,accuracy and thermal fatigue life of gears are improved.The rising of either torque or rotational speed can intensify the temperature field and thermo-elastic field of gear,and the modification amount should be designed in terms of torque in order to avoid the edge effect.