Positive displacement motors are the most commonly used drives for directional drilling operations. They contain a rubber lining, which is not only important for the functionality of the motor, but also the reason for most failures of the power section. Simulations to investigate the strains and stresses inside the rubber lining should consider the mechanical and the thermal behavior. However, since those effects occur on different time scales, a fully coupled transient simulation would not be sensible. An efficient way to simulate both aspects is an iterative algorithm including a thermal and a separate mechanical model, which are simulated in alternation until the stationary state is found. Those models require an appropriate material model taking into account the typical effects of filled rubber. Therefore, the MORPH material model by Ihlemann was extended to consider volume changing effects and the temperature dependency of the mechanical behavior of the elastomer. Moreover, a strategy to compute the heat dissipation due to hysteresis is necessary. In this contribution, the implementation of a heat dissipation calculation strategy based on closed loading cycles is presented. The modeling strategy and the computation of the hysteresis heat is validated by comparisons with real motor data from flow loop tests. During the tests, the temperature inside the stator lining at different operating states was recorded with sensors, so that the resulting temperature distribution can be compared with corresponding simulation results from the iterative algorithm. The compared data show a high correlation. In addition, the modeling strategy can be used to investigate various setups of the motor. For example, an extensive investigation of virtual materials is conducted to evaluate the impact of different elastomer properties on the strains and stresses, the temperature, and the mechanical as well as the volumetric efficiency of the motor.