A plane elastic problem of bodies bounded by concentric circles and heated at the inner boundary is solved in the "uncoupled, quasi-static" approximation. The heating takes place by surface heat transfer, with limiting cases corresponding to sudden temperature change and to constant flux of heat. The stress boundary conditions treated are those of constant flux of heat. The stress boundary conditions treated are those of constant pressure at the inner wall while the outer wall may be either free or rigidly restrained. The time-dependent results for stresses, displacement, and temperature are calculated and shown for several cases with varying values for the parameters specifying heat transfer and wall thickness. The effect of varying Poisson's ratio is also examined. Formulas for steady-state distributions of the quantities of interest are also given, as well as some approximate results that can be used for very small times.