Abstract The paper begins with a statement of a reciprocal theorem in thermoelasticity based on a generalization of Betti's reciprocal theorem. This is followed by the application to and solution of a simply supported curved plate, cut from a complete thin-walled cylindrical shell of radius a, subject to an arbitrary three-dimensional temperature distribution. The general solution is then used to determine the stresses and displacements resulting from a specified three-dimensional temperature distribution. The results are presented as non-dimensional curves. The usefulness of the theorem resides in the fact that, by appropriate application, existing solutions in elasticity may be used to obtain solutions of thermoelastic problems.