<p>We study the quasistatic thermoelastic state of a thermosensitive piecewise homogeneous structures subjected to different types of heating through the boundary surfaces and in the contact zone. To construct the solution of the nonstationary heat-conduction problem, we use a numerical-analytic approach based on the methods of successive approximation and linearizing parameters, and on the application of the adapted Prudnikov formula for the inversion of the Laplace transform. The efficiency of the proposed approach is demonstrated on the example of a problem for two layers subjected to the action of a heat source for a certain time interval on the contact boundary under the conditions of complex heat exchange with the ambient medium through the surfaces of the layers.</p>