An axial flux machine having a stator which is located between a first rotor disk and a second rotor disk. The base part of the stator is a central support flange which defines a first lateral face and a second lateral face. The central support flange has a plurality of flow openings. A first, left stator cover is mounted, with a formed collection channel, on the first lateral face of the support flange, and a second, right stator cover is mounted, with a formed distribution channel, on the second lateral face of the support flange.