The ability to rationally modify targeted physical and biological features of a protein of interest holds promise in numerous academic and industrial applications and paves the way towards de novo protein design. In particular, bioprocesses that utilize the remarkable properties of enzymes would often benefit from mutants that remain active at temperatures that are either higher or lower than the physiological temperature, while maintaining the biological activity. Many in silico methods have been developed in recent years for predicting the thermodynamic stability of mutant proteins, but very few have focused on thermostability. To bridge this gap, we developed an algorithm for predicting the best descriptor of thermostability, namely the melting temperature Tm, from the protein's... sequence and structure. Our method is applicable when the Tm of proteins homologous to the target protein are known. It is based on the design of several temperature-dependent statistical potentials, derived from datasets consisting of either mesostable or thermostable proteins. Linear combinations of these potentials have been shown to yield an estimation of the protein folding free energies at low and high temperatures, and the difference of these energies, a prediction of the melting temperature. This particular construction, that distinguishes between the interactions that contribute more than others to the stability at high temperatures and those that are more stabilizing at low T, gives better performances compared to the standard approach based on T-independent potentials which predict the thermal resistance from the thermodynamic stability. Our method has been tested on 45 proteins of known Tm that belong to 11 homologous families. The standard deviation between experimental and predicted Tm's is equal to 13.6°C in cross validation, and decreases to 8.3°C if the 6 worst predicted proteins are excluded. Possible extensions of our approach are discussed.