  Our research is directed to a quasi-static evolution of the
thermo-visco-elastic model. We assume that the material is subject to two kinds
of mechanical deformations: elastic and inelastic. Moreover, our analysis
captures the influence of the temperature on the visco-elastic properties of
the body. The novelty of the paper is the consideration of the
thermodynamically complete model to describe this kind of phenomena related
with a hardening rule of Norton-Hoff type. We provide the proof of existence of
solutions to thermo-visco-elastic model in a simplified setting, namely the
thermal expansion effects are neglected. Consequently, the coupling between the
temperature and the displacement occurs only in the constitutive function for
the evolution of the visco-elastic strain.
