A dynamoelectric machine 30 includes a rotor 32 and a stator 34 surrounding the rotor. The dynamoelectric machine 30 further includes a generator housing 36 surrounding both the rotor 32 and the stator 34. Additionally, the dynamoelectric machine 30 includes at least one blower 39a, 39b for generating a cooling gas flow 38 within the generator housing 36 to cool the stator 34 and the rotor 32. The dynamoelectric machine 30 includes at least one arcuate heat exchanger 40a, 40b, 80a, 80b within the generator housing 36 for extracting heat from the cooling gas flow 38.