  This paper is devoted to study the asymptotic expansion of the heat trace of
the Dirichlet-to-Neumann map for the thermoelastic equation on a Riemannian
manifold with doundary. By providing a method we can obtain all the
coefficients of the asymptotic expansion. In particular, we explicitly give the
first two coefficients involving the volume and the total mean curvature of the
boundary.
