Existing thermal models of asynchronous motors either require a large number of calculations and source data or have poor accuracy. Thus, it is relevant to develop methods of thermal calculation of electric motors that have adequate accuracy with a small number of calculations. To design a mathematical model of heating an asynchronous motor, methods of mathematical simulation, and the method of equivalent thermal circuits are used to calculate the temperature rise of motor parts. The authors have proposed a combined mathematical model to calculate the temperature of an asynchronous motor. It combines the method of equivalent thermal circuit and the method of calculating the temperature rise of the rotor, which allows reducing the number of nodes of the thermal circuit without increasing the simulation error. An algorithm of parallel calculation of the thermal state of the fixed part of the electric machine and the rotor has been developed. The results obtained allow us to conclude that the developed model can be used to calculate the thermal state of motors. The calculation error of the combined model is lower than when calculating using the equivalent thermal circuit method. The obtained algorithms can be improved and integrated into the general equivalent thermal circuit. It will allow us to use the proposed method to calculate the motors with a phase-wound rotor.