In conventional transient thermal‐stress analyses, the heating rates are sufficiently slow so that the inertia terms in the equations of equilibrium are negligible and time enters as a parameter from the transient temperature in the body. Recently, one has encountered extremely high heating rates and it is necessary to reexamine the role of inertia. Such studies of extremely massive infinite and semiinfinite bodies and extremely slender bodies have been made by others. In the former, thermal‐stress wave propagation without reflection was examined; in the latter, thermally induced vibrations were considered. It is of interest now to examine the effect of inertia in a body whose dimensions lie be‐between these extremes. As an example, we consider a hollow sphere of arbitrary thickness subjected to a step change of temperature on its inner surface. In the solution, the propagation and reflection of thermal‐stress waves in the sphere are observed. For comparison, the results of the conventional analysis are obtained as a special case. After passing to appropriate limits, the results are compared to previous analyses of slender and massive spherical regions.