Abstract: A heat exchanger has a header in the form of a stack consisting of pairs of shells, with the two shells of each pair being assembled together through their outer flanges, and with two adjacent shells, each belonging to a different pair, being joined together through annular inner flanges which are joined to the outer flanges of the shells through annular side walls. The outer flanges of the two shells of each pair, which define a housing for the end of an associated flattened fluid flow tube, also bear on the faces of a turbulator plate which projects out of the corresponding tube. The contact of the shells with the turbulator plate improves the rigidity of the header. The invention is applicable to the cooling of supercharging air in industrial vehicle engines.