A variational expression is devised from which the governing equations are derivable for all problems of radiant interchange between diffusely emitting and reflecting surfaces. This correspondence between the variational expression and the equations of radiant interchange serves as the basis of an approximate solution method for radiation heat transfer problems. The solution method is discussed in general and then applied to specific physical situations. It is shown that the variational method yields results with remarkable ease, especially when compared with the formidable computational task inherent in a direct numerical assault on the governing integral equations.