Low-velocity, shock-free impact is one of the accidental loads that can lead to a thermal explosion, the latter being the consequence of a chain of mechanisms depending on the microstructure of the material. To investigate the causes, the predictive capability of numerical tools depends on the physics embedded in the models. While a consensus has developed around the concept of hot spots, the exact nature of the thermo-mechanical heat-generating processes that preceded them remains to be clarified. We are studying a composition similar to the PBX 9501. HMX crystals are mixed with a few percent of a polymer binder. Recent experiments (reverse edge-on impact test) have revealed the influence of the plasticity of HMX grains even at low strain rates and low confinement. The heat released by the plastic dissipation has been identified as a potential candidate for the formation of hot spots. In this study, a numerical representation based on a polycrystalline beta-HMX material subjected to intense shear is presented. Due to the high pressure generated by the impact, the intergranular slip is ignored. Emphasis is placed on the heterogeneity resulting from the micro-structural characteristics and the interaction between the anisotropic single crystals. The behavior of the binder and the influence of other heterogeneities such as friction or micro cracks are set aside. Finally, the mechanical dissipation is calculated in the models and the maximum temperature is deduced.