The impact of solar radiation on spacecraft can increase the cooling load, degrade the material properties of the structure and possibly lead to catastrophic failure of their missions. In this paper, we develop a computational model to investigate the effect of the exposure to solar radiation on the thermal distribution of a spacecraft with a cylindrical shape which is traveling in low earth orbit environment. This is obtained by the energy conservation between the heat conduction among the spacecraft, the heating from the solar radiation, and the radiative heat dissipation into the surroundings while accounting for the dynamics of the space vehicle (rotational motion). The model is solved numerically using the meshless collocation point method to evaluate the temperature variations under different operating conditions. The meshless method is based on approximating the unknown field function and their space derivatives, by using a set of nodes, sprinkled over the spatial domain of the spacecraft wall and functions with compact support. Meshless schemes bypass the use of conventional mesh configurations and require only clouds of points, without any prior knowledge on their connectivity. This would relieve the computational burden associated with mesh generation. The simulation results are found in good agreement with those reported in previously-published research works. The numerical results show that spinning the spacecraft at appropriate rates ensures low and uniform temperature distribution on the spacecraft, treated as thick-walled object of different geometries. Therefore, this would extend its lifetime and protect all on-board electronic equipment needed to accomplish its mission.