A heat exchanger has oil core plates and coolant core plates disposed in alternating, stacked relationship. Flow passages are provided between adjacent plates, so that the oil flow passages alternate with the coolant flow passages, and the oil can flow from an oil inlet opening of each oil plate, and through the oil flow passage to an oil outlet opening, and coolant can flow from a coolant inlet opening of each coolant plate through the coolant flow passage to a coolant outlet opening. The oil inlet openings are adjacent to one end of the plates, and the oil outlet openings are spaced from the oil inlet openings, with a passageway for flow of the oil between upstanding bosses of the coolant plates on opposed sides of each oil plate and extending from a gap in an upstanding flange of the oil plate to the oil outlet opening.