The heat exchanger is enclosed in a casing (1) in which the outlet aperture (2) of the catalytic converter (3) comes out. Thermal insulation is fitted round a through tube (7) at a spacing from the catalytic converter, with inlet (8) and outlet (9) apertures. The inlet aperture (8) of this tube and the outlet aperture (3) of the catalytic converter are facing each other. The space between the through tube and the casing wall is filled with insulation. It has heat exchange tubes (11) for the exhaust gas (A) and acts with a device by which the outlet aperture of the through tube can be wholly or partly closed. The casing has an outlet aperture (13) for the exhaust gas.