  This paper deals with the large-time analysis of a PDE system modelling
contact with adhesion, in the case when thermal effects are taken into account.
The phenomenon of adhesive contact is described in terms of phase transitions
for a surface damage model proposed by M. Fremond.
  Thermal effects are governed by entropy balance laws. The resulting system is
highly nonlinear, mainly due to the presence of internal constraints on the
physical variables and the coupling of equations written in a domain and on a
contact surface. We prove existence of solutions on the whole time interval
$(0,+\infty)$ by a double approximation procedure. Hence, we are able to show
that solution trajectories admit cluster points which fulfil the stationary
problem associated with the evolutionary system, and that in the large-time
limit dissipation vanishes.
