The exhaust gas supercharger comprises a compressor (2) coupled to an exhaust gas turbine and has a cooling device (30) that consists of at least one supply channel (31) connected to the lubricating oil system of the supercharger. The cooling device has also a distribution device (32) which is connected to the supply channel. The distribution device is fitted in the turbine side of the intermediate wall (24). The supply channel blends into an annular channel (33) which is connected to the distribution device by at least one channel (34).