A multiscale model is formulated and used to characterize the duration and amplitude of temperature peaks (i.e., hot spots) at intergranular contact surfaces generated by shock compaction of the granular high explosive HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine). The model tracks the evolution of both bulk variables and localized temperature subject to a consistent thermal energy localization strategy that accounts for inelastic and compressive heating, phase change, and thermal conduction at the grain scale (grain size ). Steady subsonic compaction waves having a dispersed two-wave structure are predicted for mild impact of dense HMX (porosity ), and steady supersonic compaction waves having a discontinuous solid shock followed by a thin compaction zone are predicted for stronger impact. Short duration hot spots having peak temperatures in excess of are predicted near intergranular contact surfaces for impact speeds as low as ; these hot spots are sufficient to induce sustained combustion as determined by a two-phase thermal explosion theory. Thermal conduction and phase change significantly affect hot-spot formation for low impact speeds , whereas bulk inelastic heating dominates the thermal response at higher speeds resulting in longer duration hot spots. Compressive grain heating is shown to be largely inconsequential for the range of impact speeds considered in this work . Predictions for the variation in inelastic strain, pressure, and porosity through the compaction zone are also shown to qualitatively agree with the results of detailed mesoscale simulations.