<p>We solve the nonstationary problem of heat conduction for two contacting thermosensitive layers under the conditions of complex heat exchange with ambient media. The solution is obtained by using the analytical-numerical approach based on the application of a version of the methods of successive approximations, linearizing parameters, Laplace integral transform, and its numerical inversion with the help of the Prudnikov formula adapted to the problems of heat conduction. We investigate the thermal state of the outlined thermosensitive piecewise-homogeneous structure for different combinations of boundary conditions on its surfaces.</p>