A cooling body for the regulator of an electric machine, which regulator may be a voltage regulator of a DC generator of a vehicle, includes a heat exchange surface with an inflow region and an outflow region. A cooling air flow may be applied to the heat exchange surface during the operation of the electric machine. The cooling air stream impinges on the heat exchange surface in the inflow region and leaves the heat exchange surface from the outflow region. The heat exchange surface is shaped differently in the inflow region than in the outflow region. Because of the shape of the heat exchange surface, the direction in which the cooling air is applied is different compared to conventional surfaces.