We have used constant pressure molecular dynamics calculations to explore the behavior at various temperatures of two molecular crystals: benzene and a brominated phenyl compound. We observed a melting transition by heating the crystals from a low temperature. In the case of benzene, we performed one heating run of about 1 ns and obtained agreement with the experimental melting point to within some 8%. We have also simulated the melting of a more complex molecular crystal that contains bromine and phenyl groups. We performed four heating runs, with different rates of heating. For total simulation times of about 100, 220, 770, and 1 I50ps, the heating runs predicted melting temperatures that differed from the experimental melting temperature by 53%, 33%, 25%, and 9% respectively.