The paper deals with the general choices and the sizing problematics of a prototype of a permanent magnet synchronous machine able to work permanently at high internal temperatures, up to 500° C. The specific physical problems are listed and analyzed. The first challenge consists in defining and testing High Temperature (HT°) inorganic coils, built without any polymer. The chosen materials are able to withstand permanently such high temperatures but they have poor mechanical properties. The proposed Electrical Insulation System (EIS) is based on a thin ceramic coating for the wire and a HT ° cement for protecting the brittle ceramic insulation layer between the turns. The second challenge consists in defining the stator core and the magnets that corresponds to the HT ° inorganic rigid coils that must be built separately. Comparing to the usual approach, the design process is reversed: the magnetic circuit must be designed according to the characteristics of the HT ° coils.