This paper presents a solution for a number of problems on calculation of composite radiative-molecular heat exchange in flat, cylindrical, and spherical systems with perforated screens in conditions of free-molecular flow. Given is an analysis of the influence of certain values, as screen perforation degree, disposition of the screen in the system, absorptivity and emissivity, accomodation coefficients of heat exchanging surfaces as well as their temperature level and pressure on the net heat transfer in studied systems.