A modeling technique is described for estimating the intensity of mechanically induced thermal and combustion fluctuations at the grain scale (mesoscale) of granular energetic solids in a manner compatible with thermodynamics, contact mechanics, and bulk (macroscale) experiments. The technique is illustrated for the dynamic compaction, localized heating, and ignition of the commonly used high-explosive HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) due to mild impact by a constant-speed piston (< 150 m/s). Guided by contact mechanics, bulk dissipated mechanical energy is thermalized at localization sites (hot spots) within the material mesostructure that are centered at intergranular contact surfaces. The evolution of the bulk material response is tracked, and the corresponding evolution of hot-spot temperature, mass fraction, and reaction progress is resolved at the grain scale. Importantly, the bulk and grain-scale descriptions are energetically equivalent. Model predictions indicate that the onset of sustained combustion occurs for a piston speed that agrees well with confined deflagration-to-detonation transition experiments (&SIM;86 m/s). Also, the model is shown to be reasonably insensitive to variations in key energy localization parameters. Consequently, the technique may provide a rational framework for the development and assessment of mechanical ignition models based on hot-spot formation.