A model is presented for time and spatial dependences of the heating of molecular vibrations and the possible initiation of chemical reaction from heat dissipated in the vicinity of a propagating crack in a molecular crystal. In the model, energy from a moving crack tip is released as phonons in proximity to the crack. Initially the phonons and the molecular vibrations are not in thermal equilibrium. Subsequently, there is a competition between excitation of molecular vibrations by multiphonon up-pumping and diffusion of phonons from the crack region. If the coupling between the locally hot phonon bath and the molecular vibrations is sufficiently large, a transitory high vibrational temperature will be achieved prior to eventual thermal equilibration with the bulk of the crystal. It is found that the peak vibrational temperature can be sufficiently high for a significant time period for chemical reactions to occur. The model calculates the local time-dependent vibrational temperature using reasonable values of the physical input parameters. For a crack tip moving near the speed of sound, the calculations show that vibrational temperatures can reach similar to 800 K in 55 ps and exceed 550 K for similar to 1 ns after the initial heating. This temperature change is sufficient to produce chemical reaction in a secondary explosive such as HMX, but given the duration and size of the heated region, a single crack should not result in self-sustaining chemical reaction. The role that cracks may play in shock sensitivity is discussed.