  In this paper, we study a system of thermoelasticity with a degenerated
second order operator in the Heat equation. We analyze the evolution of the
energy density of a family of solutions. We consider two cases: when the set of
points where the ellipticity of the Heat operator fails is included in a
hypersurface and when it is an open set. In the first case and under special
assumptions, we prove that the evolution of the energy density is the one of a
damped wave equation: propagation along the rays of geometric optic and damping
according to a microlocal process. In the second case, we show that the energy
density propagates along rays which are distortions of the rays of geometric
optic.
