The electromagnetic field enhancement (FE) at the end of the probe of an Apertureless Scanning Near-field Optical Microscope (ASNOM) is used to write nanometric dots in a phase-change medium. The FE acts as a heat source that allows the transition from amorphous to crystalline phase in a Ge2Sb2Te5 layer. Through the 2D Finite Element Method (FEM) we predict the size of the dot as a function of both the illumination duration and the incoming power density. Numerical results are found to be in good agreement with preliminary experimental data.