We propose a method for the construction of analytic-numerical solutions of nonstationary problems of heat conduction for the case of contact of thermosensitive bodies of simple shape (flat, cylindrical, or spherical) with heat exchange with the ambient medium through the surfaces of the bodies. It is assumed that the thermal diffusivity is constant. We construct the solution of a nonstationary problem of heat conduction for a system formed by a cylindrical body with thin coating heated by the ambient medium in the process of convective beat exchange through the surface of the coating. The thermal contact between the cylinder and the coating is regarded as perfect. The solution of the corresponding quasistatic problem of thermoelasticity is constructed by the perturbation method. The numerical analysis of the results is performed.
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