  We study a quasi-static evolution of thermo-visco-elastic model. We act with
external forces on non-homogeneous material body, which is a subject of our
research. Such action may cause deformation of this body and may change its
temperature. Mechanical part of the model contains two kinds of deformation:
elastic and visco-elastic. Mechanical deformation is coupled with the
temperature and they may influence each other. Since constitutive function on
evolution of visco-elastic deformation depends on temperature, the
visco-elastic properties of material also depend on temperature. We consider
the thermodynamically complete model related to hardening rule with growth
condition in generalized Orlicz spaces. We provide the proof of existence of
solutions for such class of models.
