There are a lot of well-known shock compression models for polymer materials that exploit equations of state for polymeric media with wide ranges of parameters. The models are in a good agreement with experimental data regarding the evolution of kinematic parameters of the shock compression process. However, thermodynamic parameters calculation, e.g. shock compression temperature, is less than perfect. Besides, experimental approaches for measuring the temperature are not consistent with each other, thus complicating even more the issue. Under these circumstances, development of appropriate equations of state and models for accurate evaluation of kinematic and thermodynamic parameters of polymer shock compression is of great importance. The model developed and proposed in this paper is based on Maxwell concepts of nonreversible deformation mechanisms and experimental measurement of brightness temperatures of several shock compressed polymers. Good agreement is obtained between calculations of temperature behind shock wave front and experimental measurements for polymethylmethacrylate, polytetrafluoroethylene and epoxy resin. The model calculations are compared with results calculated with other well-known equations of state, and applicability of the proposed model is demonstrated. Several problems of polymer shock wave deformation are solved.