A heat exchanger useful for high temperature applications such as EGR cooling and fuel reformer applications comprises a tube bundle made up of a plurality of tubes, each having at least one end expanded to an enlarged polygonal cross-section, and having central portions with a generally smaller cross section. When the tubes are formed into a bundle, the enlarged end portions nest with one another and interstitial spaces are provided between the central portions of the tube. The enlarged end portions are preferably retained by a header ring having a multifaceted inner peripheral sidewall which is adapted to form brazed lap joints with the outward facing surfaces of the peripheral tubes end portions in the tube bundle. In one preferred arrangement, axially aligned enlarged portions are provided intermediate the ends of at least some of the tubes. These enlarged intermediate portions nest with one another and eliminate or reduce the need for baffle plates.