Special semidiscrete approximations, namely, basic, first, and second semidiscrete problems are proposed for a boundary value problem describing a stationary radiative–conductive heat transfer in a two-dimensional system of heat-conductive plates of width ɛ separated by vacuum interlayers. We prove the unique solvability for the first and second semidiscrete problems, establish a comparison theorem, and obtain estimates of their solutions. For the first semidiscrete problem we also obtain some results concerning stability and derive an error estimate of order O(ɛ). Results of numerical experiments are presented.