Abstract <p>The paper proposes a mathematical model and an effective approximate-analytical method for solving the problem of thermal protection against solar radiation for an orbital spacecraft (SC) in the form of a system of thin plates with low emissivity, coupled with inertial thermal insulation. The air is evacuated from the spaces between the plates, so heat exchange between the plates occurs via radiation with re-radiation, accounting for temperature changes in the plates due to volumetric heat capacity. The goal of the mathematical modeling is the optimal selection of the number of plates, their thicknesses, and the thickness of inertial insulation to achieve a comfortable temperature inside the SC’s hull. The mathematical model is presented as a normal system of strongly nonlinear ordinary differential equations (ODEs). The approximate-analytical method consists of two stages: in the first stage, differential operators are approximated as finite-difference ratios, and a system of algebraic equations is derived, from which a set of fourth-degree equations for temperatures at the upper time layer is isolated, each solvable exactly in radicals. In the second stage, the obtained temperature values are substituted into the original system of algebraic equations, which becomes a system of linear algebraic equations with a tridiagonal matrix solvable by the Thomas algorithm. The results of numerical calculations are obtained and analyzed</p>