We present a simulation study of the thermal behaviour of the moderator and the electrostatic lens of the positron source EPOS at the Research Center Dresden-Rossendorf. The positron moderator and the upper part of the electrostatic extraction einzellens are directly exposed to the primary electron beam with an energy of 40 MeV and a current of 1 mA. Thus, it was necessary to investigate whether the construction can stand the high temperatures. As a result we found that thin moderator foils with a thickness less than 40 μm will not reach too high temperatures. The thickness can be varied up to 0.2 mm, so we adjust the temperature in order to anneal lattice defects. These defects are caused by radiation. The wall of the extraction lens which is made from a stainless steel tube must be distinctly thinned to 0.05 mm to avoid damage temperatures. The time-dependent simulation shows, that the final temperatures are reached after less than a minute.