A device for cooling an exhaust gas stream, having an exhaust gas pipe receiving the exhaust gas stream, the exhaust gas pipe being surrounded at least in places by a heat shield arranged spaced therefrom, which together with the outside of the exhaust gas pipe forms a convection region for air supplied from the surrounding environment. A mouth region of the exhaust gas pipe extended relative to the heat shield projects in such a way into an open end of an adjoining outlet port that a reduced pressure relative to the surrounding environment may be produced in a suction region between the mouth region of the exhaust gas pipe and the outlet port as the air heated in the convection region due to the exhaust gas stream rises.