The study of the Moon has been of great interest to several countries, due to several factors, such as, mining valuable resources and building lunar outposts, which would open up new perspectives for deep-space explorations. Lunar outposts, obviously, would need power plants to provide them with energy, therefore the research of lunar power plants to be implemented on the moon is considered important. In this paper, the free-piston Stirling engine, whose principle of operation is based on an external supply of thermal energy, is adopted as the basic engine design and a schematic diagram of the power plant is developed. Moreover, a method for calculating the heat balance of the radiator is proposed, and a computational study of the influence of the materials’ and refrigerants’, main constructive and thermo-physical properties on the efficiency of the radiator is carried out. In conclusion, the dependences of the radiator size on the pressure, flow velocities and physicochemical properties of the refrigerant are obtained. © 2021, Univelt Inc. All rights reserved.