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When designing a temperature control system (TCS) of a spacecraft propulsion system, it is necessary to calculate the flow distribution of the coolant taking into account changes in the flow temperature. The coolant flow in the TCS is non-isothermal and mass flow can differ by a huge ratio in various lines. With this formulation, many explicit numerical methods for solving the flow distribution problem become unstable. In this paper, we propose a method for the numerical solution of a hydrostatic problem for a branched pneumatic-hydraulic system represented by a graph with nonlinear connections. The main advantage of the method is the possibility of solving nonlinear equations describing the hydraulic lines by implicit numerical methods. The method allows the use of experimental dependences and preliminary resource-intensive numerical modeling of complex elements (for example, solving the Navier-Stokes equation with turbulence models) to solve the entire pneumatic-hydraulic system. [ABSTRACT FROM AUTHOR]