  We present and analyze a high-order discontinuous Galerkin method for the
space discretization of the wave propagation model in thermo-poroelastic media.
The proposed scheme supports general polytopal grids. Stability analysis and
$hp$-version error estimates in suitable energy norms are derived for the
semi-discrete problem. The fully-discrete scheme is then obtained based on
employing an implicit Newmark-$\beta$ time integration scheme. A wide set of
numerical simulations is reported, both for the verification of the theoretical
estimates and for examples of physical interest. A comparison with the results
of the poroelastic model is provided too, highlighting the differences between
the predictive capabilities of the two models.
