Melting point is one of the most fundamental and practically important properties of a compound. Molecular simulation methods have been developed for the accurate computation of melting points. However, all of these methods need an experimental crystal structure as input, which means that such calculations are not really predictive since the melting point can be measured easily in experiments once a crystal structure is known. On the other hand, crystal structure prediction (CSP) has become an active field and significant progress has been made, although challenges still exist. One of the main challenges is the existence of many crystal structures (polymorphs) that are very close in energy. Thermal effects and kinetic factors make the situation even more complicated, such that it is still not trivial to predict experimental crystal structures. In this work, we exploit the fact that free energy differences are often small between crystal structures. We show that accurate melting point predictions can be made by using a reasonable crystal structure from CSP as a starting point for a free energy-based melting point calculation. The key is that most crystal structures predicted by CSP have free energies that are close to that of the experimental structure. The proposed method was tested on two rigid molecules and the results suggest that a fully in silico melting point prediction method is possible.