The models for one space dimension discussed in the previous chapter demonstrated that the behavior of the nonlinear thermoelastic system is dominated by the heat conduction at least with respect to the existence of solutions for small data. We also know already that the decay of solutions to the linearized equations in more than one space dimension has a strong hyperbolic feature. Only for symmetric situations like radial symmetry in bounded domains or for the Cauchy problem for isotropic (or cubic) media could decay rates be given, for the latter with a hyperbolic part, for the former with an exponential decay result.