A general analysis is developed for the complete three-dimensional transient thermal-stress distribution in a finite circular cylinder subject to arbitrary heating of the lateral surface with arbitrary heat transfer into the surrounding medium. The problem is formulated in terms of the modified Boussinesq functions and the thermoelastic displacement potential, which seem convenient in form and have the advantage of being applicable to non-axisymmetric problems. The solution meets the tractionfree boundary conditions on both the lateral surface and the plane ends of the cylinder. Graphical illustrations are provided.