The advancing requirements for strength, relaxation, thermophysical, electrical, and other structural elements characteristics actualizes the polymer composite material use for the soft part and node point manufacture, which improves performance index. This paper reported the need to take into account relaxation phenomena in predicting the body’s thermal field development that is made of polymeric materials, and the thermal relaxation time and the thermal damping time proportional to the duration of transient thermal process certain periods. In this article three-period thermal process in a cylindrical body mathematical model is presented. cylindrical body made of a low-heat-conducting material by using a heat conduction hyperbolic equation that is reflecting the heat flow relaxation and thermal damping phenomenon. A numerical solution to the problem of unsteady heat conduction in a circular disk for a two-phase delay equation is presented, which is based on the grid method implementation by using a three-layer implicit difference scheme and the finite difference method use. Calculation formulas for the run-through coefficients as well as the temperature values at the outer boundaries are concluded using the boundary conditions approximation for the intermediate and upper time layers, taking into account the multi-period of the process. The implementation of the modified run-through method when solving the non-stationary heat conduction problem in a cylindrical body, taking into account the finite heat propagation speed and thermal damping is described. The calculation results for the cylindrical body temperature field are obtained by using the polymethyl methacrylate example upon sudden heating based on a model with a two-phase delay. The results presented in this paper aid in an increase in predicting temperature field accuracy in polymer composite materials in the transient thermal processes study.

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