The objective of this work is to improve the robustness and accuracy of numerical simulations of both ideal and non-ideal explosives by introducing temperature dependence in mechanical equations of state for reactants and products. To this end, we modify existing mechanical equations of state to appropriately approximate the temperature in the reaction zone. Mechanical equations of state of Mie-Grüneisen form are developed with extensions, which allow the temperature to be evaluated appropriately, and the temperature equilibrium condition to be applied robustly. Furthermore the snow plow model is used to capture the effect of porosity on the reactants equation of state. We apply the methodology to predict the velocity of compliantly confined detonation waves. Once reaction rates are calibrated for unconfined detonation velocities, simulations of confined rate sticks and slabs are performed, and the experimental detonation velocities are matched without further parameter alteration, demonstrating the predictive capability of our simulations. We apply the same methodology to both ideal (PBX9502, a high explosive with principal ingredient TATB) and non-ideal (EM120D, an ANE or ammonium nitrate based emulsion) explosives.