The main purpose of this article is to determine the field of temperature axial symmetrically distributed on thick cylindrical metalopolymeric layers, created by a constant temperature given on one of the two circular contours, by the heat flux given the other contour and by a constant inner heat source. Also, analytical expressions are obtained for both thermo-elastic displacements, and the thermal stresses, created by the temperature field, by the contour displacement, and by the pressure given on the other circular contour of the cylinder. For the determination of the temperature field and for determination of the fields of thermo-elastic displacements and of the thermal stress it has been applied to the Green’s functions method. To achieve this aim we construct the Green’s functions and then using them and some integral formulas, allowed us to obtain analytical expressions for field of temperature and fields thermo-elastic displacements and of thermal stresses. Both analytical expressions for constructed Green’s functions and analytical expressions for displacements and thermal stresses satisfy exactly the basic differential equations, the boundary conditions and conjugation conditions. The obtained results will be used both for the determination of thermal conductivity of the contact area, and for determination the thermo-elastic displacements and thermal stresses necessary for calculations of the strength and rigidity of the parts reconditioned by compensating wear of composite material applied in layers thick.