Abstract: An improved apparatus is provided to cool the flux shields of dynamoelectric machines. In one embodiment of this invention, cooling fins are attached to a flux shield at localized areas of heating of the flux shield referred to as hot spots to reduce the temperatures there to acceptable levels. These fins may be provided with a tapered portion which minimizes the fluid losses associated with the flow of cooling gas over the fins. In another embodiment of the present invention, an annular rim, bored to provide cooling gas passages therethrough, is fixed to the flux shield along an inner portion thereof, to effect the transfer of heat from the flux shield to a flow of the cooling gas through the passages. Finally, in a third embodiment of the present invention, an electrically non-conducting annular baffle is disposed around the flux shield adjacent an inner surface thereof to direct a flow of cooling gas across the inner surface of the flux shield thereby cooling the same.