  We study the system of nonisentropic thermoelasticity describing the motion
of thermoelastic nonconductors of heat in two and three spatial dimensions,
where the frame-indifferent constitutive relation generalizes that for
compressible neo-Hookean materials. Thermoelastic contact discontinuities are
characteristic discontinuities for which the velocity is continuous across the
discontinuity interface. Mathematically, this renders a nonlinear
multidimensional hyperbolic problem with a characteristic free boundary. We
identify a stability condition on the piecewise constant background states and
establish the linear stability of thermoelastic contact discontinuities in the
sense that the variable coefficient linearized problem satisfies a priori tame
estimates in the usual Sobolev spaces under small perturbations. Our tame
estimates for the linearized problem do not break down when the strength of
thermoelastic contact discontinuities tends to zero. The missing normal
derivatives are recovered from the estimates of several quantities relating to
physical involutions. In the estimate of tangential derivatives, there is a
significant new difficulty, namely the presence of characteristic variables in
the boundary conditions. To overcome this difficulty, we explore an intrinsic
cancellation effect, which reduces the boundary terms to an instant integral.
Then we can absorb the instant integral into the instant tangential energy by
means of the interpolation argument and an explicit estimate for the traces on
the hyperplane.
