Two-dimensional thermoelastic problems under axisymmetric temperature distributions are considered within the context of the theory of generalized thermoelasticity with one relaxation time. The general solution is obtained in the Laplace transform domain by using a direct approach without the customary use of potential functions. The resulting formulation is used to solve two problems of a solid sphere and of an infinite space with a spherical cavity. The surface in each case is taken to be tractionfree and subjected to a given axisymmetric temperature distribution.