A reliable control of current orientation of a spacecraft is a critical task in aerospace engineering, as the loss of the spacecraft’s attitude can endanger the whole mission. This makes it important to elaborate on a reliable and robust attitude control system of a spacecraft, which can extend its lifetime. It must have a simple design, and low mass and power consumption. To develop it, we use various conditions of radiative heating at the surface of the spacecraft’s elements with different directions to the Sun and a planet that a satellite orbits to estimate their angular position. In the case of slow angular velocity of a spacecraft, temperature measurements can be used to estimate integral (over the spectrum) radiative flux using specially designed thermal sensors at different convex surfaces of a spacecraft. Then the estimated heat fluxes can be used to determine the attitude of a spacecraft. To provide this approach, it is essential to consider two inverse problems of heat transfer. Thus, the authors aim to solve these problems, which are challenging. This paper is dedicated to the solution of the second inverse problem. It was shown that one can obtain sufficiently accurate results on the basis of a constrained set of relatively simple temperature measurements.