Abstract: A fan has a motor, a fan impeller, a cooling body and a housing. The motor is electrically driven and has a stator and has a rotor which is mounted so as to be rotatable about an axis of rotation, wherein the motor has at least one winding through which an electrical current flows during operation. The fan impeller is fastened rotationally conjointly to the rotor and serves for drawing in and conveying a gaseous medium. The cooling body has an inner wall which delimits an interior space for accommodating the motor, and has air-guiding elements which extend in each case in an axial direction over a major part of the longitudinal extent of the winding, through which electrical current flows, in order to conduct the gaseous medium, which is conveyed by the fan impeller, along the cooling body for motor cooling purposes. The housing has an outer wall which delimits a cavity for accommodating the cooling body and the motor.