An air-to-air cooler has a heat exchanger integrated to a housing. A first passage extends through the housing for directing a flow of cooling air through the heat exchanger. A second passage extends through the housing for directing a flow of hot air to be cooled through the heat exchanger. The first passage has a cooling air outlet tube disposed downstream of the heat exchanger. The cooling air outlet tube extends across the second passage between the heat exchanger and a hot air inlet of the second passage. The hot air inlet is disposed to cause incoming hot air to flow over the cooling air outlet tube upstream of the heat exchanger. An ejector drives the flow of cooling air through the first passage of the air-to-air cooler. A portion of the hot air flow may be used to drive the ejector.