The Galerkin method is extended to study the interaction of thermal radiation and heat conduction between two concentric spheres separated by an absorbing, emitting, isotropically scattering and heat generating gray medium. The boundaries are maintained at different but uniform temperatures, and are considered to be opaque, gray, diffusely emitting and diffusely reflecting. A superposition technique is used to decompose the problem into three simpler problems. Each simple problem is solved by the Galerkin method. The effects of optical thickness, scattering, boundary reflectivities, boundary temperatures, and the conduction-to-radiation parameter on the temperature distribution and the transfer of thermal energy are investigated. Results are compared with the numerical results available in the literature. It is shown that the method is relatively simple in problems with spherical symmetry and yields highly accurate results.