The oil cooler consists of several bath-shaped plates (2) stacked and soldered to each other to form adjacent chambers (3,4) with their high-standing edges (2a). The lowest plate (2') is fitted to a baseplate (17). There is a reinforcement plate between the baseplate and the lowest plate. The reinforcement plate has a border gripping the edge of the lowest plate. This border has the form of upright tabs which lie only against the longitudinal and transverse sides of the edge of the rectangular plate (2').