Modelling the extraneous heat exchange of spacecraft using solar radiation simulation facility and simulators of the planetary radiation field in several cases is an intractable problem not only in technical but also in methodological terms. For some technical reasons, solar radiation simulator is stationary. Consequently, to reproduce a possible change in the orientation of the test object relative to the solar radiation flux, it is necessary to equip the thermal vacuum unit with devices that allow the test object to be rotated at least about two axes. In this paper, a mathematical model and a method for solving the problem of heat transfer in a multilayer structure of screen-vacuum thermal insulation under the influence of solar radiation is proposed. A method is proposed for the numerical solution of a normal system of nonlinear differential equations using the linearisation of nonlinear terms. Various results of numerical modelling were obtained, which indicate the adequacy of the proposed mathematical model. It has been revealed that high-inertia thermal insulation of sufficient thickness is required to stabilise the thermal state inside the spacecraft.