The specification discloses a heat exchanger adapted to be coupled between the exhaust outlet of a room heating unit and a chimney for extracting heat from the exhaust gases flowing therethrough and returning the same to the room. The heat exchanger includes a plurality of vertically spaced rows of horizontally extending exhaust conveying tubes. End caps couple adjacent ends of the tubes to form an upwardly progressing serpentine path for the exhaust gases. A shroud structure separately houses individual vertically spaced clusters of the tubes so that air flows by convection generally horizontally past the tubes. Heat exchange efficiency is improved since a fan is not utilized and since the higher tubes do not come into contact with air already heated by the lower tubes.