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A multiscale modeling strategy is used to quantify factors governing the temperature rise in hot spots formed by pore collapse from supported and unsupported shock waves in the high explosive HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine). Two physical aspects are examined in detail, namely the melting temperature and liquid shear viscosity. All-atom molecular dynamics simulations of phase coexistence are used to predict the pressure-dependent melting temperature up to 5~GPa. Equilibrium simulations and the Green-Kubo formalism are used to obtain the temperature- and pressure-dependent liquid shear viscosity. Starting from a simplified continuum-based grain-scale model for HMX, we systematically increase the complexity of treatments for the solid-liquid phase transition and liquid shear viscosity in simulations of pore collapse. Using a realistic pressure-dependent melting temperature completely suppresses melting for supported shocks, which is otherwise predicted when treating it as a constant determined at atmospheric pressure. Alternatively, large melt pools form around pores during pressure release in unsupported shocks, even with a pressure-dependent melting temperature. Capturing the pressure dependence of the shear viscosity increases the peak temperature of melt pools by hundreds of Kelvin through viscous work. The complicated interplay of the solid-phase plastic work, solid-liquid phase transition, and liquid-phase viscous work identified here motivate taking a systematic approach to building increasingly complex grain-scale models and for guiding interpretation of predictions made using them.