In a rotating electrical machine having a permanent-magnet rotor, the tubular, highly thermally conductive supporting body of the stator forms a thermal bridge to a cooling means. In order to allow the end windings of the stator windings to be cooled effectively as well, the end windings also each have an associated thermal bridge, which completely fills the space between the end windings and the supporting body of the stator. This thermal bridge is of solid construction having a solid ring, which is connected to the supporting body of the stator with a force fit, and a cast-resin body which is cast into this solid ring. The cast-resin body has a thermal conductivity of more than 1.6 W/mK and, for this purpose, contains a powdery, highly thermally conductive filler making up a proportion of 50 to 90% by weight, preferably an aluminum nitride coated with silicon dioxide.