This work presents a mechanical model for simulating the anisothermal behavior of damageable inelastic solids under dynamical loadings. The main motivation of this study is to investigate, by means of numerical simulations, the thermomechanical coupling in a simple one-dimensional problem involving the wave propagation phenomenon in a damageable non-isothermal solid. To achieve this goal, the equation of energy is taken into account in the modeling with the coupling terms between the thermal and mechanical effects. The damageable inelastic mechanical behavior is describe by means of an internal variable constitutive theory and the analysis is restricted to elastoviscoplastic solids. The resulting system of non linear partial differential equations is solved by using an operator splitting technique, along with classical numerical procedures such as the Glimm s method. Numerical examples which illustrate the damage and temperature evolution induced by the plastic deformation process due to impact and cyclic loadings are presented and analyzed. A suitable comparative analysis between simulations with and without the thermomechanical couplings shows the situations under which these terms are relevant.