A cooling device for cooling an air-permeable winding braid of an electrical machine is provided. The cooling device includes a baffle and a fan, which is arranged for blowing a stream of cooling air substantially perpendicularly onto a first surface portion of one side of the wind braid, wherein, in the region of a second surface portion of the side of the winding braid, arranged alongside the first surface portion, the baffle is arranged substantially parallel to and that a distance from the surface of the second surface portion such that a partial stream of the stream of cooling air is formed in the channel that is formed by the baffle and the second surface portion, and so, on the side of the winding braid that is opposite from the first-mentioned side, the other partial stream of the stream of cooling air, penetrating the winding braid, flows away from the winding braid without any return flow.