A cooling apparatus is provided for an AC generator, particularly for a transverse-flow generator having a stator with at least one armature winding, as well as a rotor disposed opposite the armature winding. Collector rings are secured to a carrier disk attached to a rotor shaft. The collector rings have a plurality of polarized magnets and magnetizable collector elements in alternating sequence disposed therein. At least one cooling channel through which a coolant can flow is provided in the vicinity of the carrier disk. The cooling channel is separated from the carrier disk only by a channel cover which has a minimal thickness and by the air gap between the rotor and the stator.