In this paper, we propose an extended model for the numerical simulation of evaporating droplets within the framework of interface capturing or interface tracking methods. Most existing works make several limiting assumptions that need to be overcome for a more accurate description of the evaporation of droplets. In particular, the variations of several physical variables with local temperature and mass fraction fields must be accounted for in order to perform more realistic computations. While taking into account the variations of some of these physical properties, as viscosity, seems rather obvious, variations of other variables, as density and surface tension, involve additional source terms in the fundamental equations for which a suitable discretization must be developed. The paper presents a numerical strategy to account for such an extended model along with several original test-cases allowing to demonstrate both the accuracy of the proposed numerical schemes and the strong interest in developing such an extended model for the simulation of droplet evaporation. In particular, the impact of thermo-capillary convection will be highlighted on the vapor film thickness between a superheated wall and a static Leidenfrost droplet levitating above this wall.