The article presents mathematical and physical modeling of the thermal-hydraulic flow of the working fluid of a hydraulic power steering (GRU) of a car based on the theory of power flow. The article describes a technique for applying the theory of power flow to the analysis of the hydraulic circuit of the power steering, which allows at the macrolevel to determine the main speed, power and power factors of calculation. As a result, for the first time, using the systems of equations of thermal and hydraulic power balances, a mathematical model of the temperature difference of the GRU working fluid was obtained, which made it possible to determine the analytical relationship between the temperature regime and efficiency, bypassing the calculation of power losses directly. The resulting mathematical model is the basis for calculating the thermal balance of the hydraulic power steering. In addition, a physical model of the pressure regulator of the working fluid in the GRU has been developed in the work, the use of which makes it possible to increase the efficiency of the GRU at the maximum allowable pressure.