Heat exchanging contact of water and blood with a pleated metal bellow heat exchanging surface in a heat exchanger for an extracorporeal blood circuit is improved by so forming the pleats of the bellows that the fluid chamber inside each pleat continuously narrows from the mouth of the pleat toward the inner end of the chamber. Uniform water distribution along the bellows is accomplished by making the water manifold in the heat exchanger core much larger in cross section than the inlet fitting to the manifold.