A fixed domain numerical scheme for ablation problems based on the enthalpy formulation and with temperature as the main dependent variable is presented. A fictitious material which occupies the region where the material has been removed is introduced, and its material properties are : null specific heat and any value for the conductivity, preferably that of the lower temperature phase. The ablating surface is transformed on an internal interface and the thermal load there is represented as a concentrated internal heat source on the interface. The resulting two-phase Stefan problem is discretized with the scheme presented in a series of previous papers. Finally, several numerical examples are presented.