In this article we present the mathematical model leading to the equations of the thermoviscoelastic coupling for large deformations. We have chosen a Poynting-Thomson model to describe the rheological behavior of the material. In this model the source term generated by viscous frictions is independent of temperature. The two-dimensional heat transfer equation in Lagrangian form is solved via a finite element method for a two-layer elastomer-metal test piece under a shear force. The results of the numerical model are compared with experimental results which show that the source term cannot be temperature independent. For a more accurate description of the real behavior of the material the source term is then identified from experimental results via an inverse method. The numerical results agree well with the experimental ones.