<p>We establish analytic expressions for the thermal displacements and stresses in a cylindrical coordinate system in the axisymmetric case. The general solution of equations of the axisymmetric theory of thermoelasticity is presented in terms of three harmonic functions. We solve the heat-conduction problem for a cylinder with thermally insulated lateral surface and heat exchange according to the Newton law on the end face. We compute the corresponding thermal displacements and stresses in the cylinder with the help of an algorithm based on the decomposition of the general thermoelastic state of the cylinder into a temperature state (depending only on temperature) and an elastic stressed state, with the use of complete systems of nonorthogonal functions and satisfying all boundary conditions as a result of minimization of the generalized quadratic form. It is shown that, for the temperature solutions of the system of Navier equations for the 3D static boundary-value problems of thermoelasticity, the sum of the normal stresses is equal to zero.</p>