The ion induced desorption is a severe luminosity limitation for low charge state heavy ion accelerators. Therefore it was intensively investigated in dedicated experiments during the last years. Several experimental results were obtained providing numerous desorption yields for different ion beam parameters and different materials as well as surface treatments. The heavy ion induced desorption was identified as a pure surface effect. Nevertheless it was shown that the yields have a strong link to the irradiated material. Furthermore it was observed that the ion beam is cleaning the sample. After desorbing a number of gas molecules corresponding to one monolayer of gas under the beam spot the sample is cleaned and the ion induced desorption is minimized. With the geometrical cross section of a projectile ion a desorption yield of several hundred molecules per ion from a monolayer is hard to explain. Therefore we have expanded the inelastic Thermal Spike Model to describe the process as thermal desorption from a microscopic heated region. The obtained results of this new model represent very well the numbers from many experimental studies.