A heat exchanger (7) for an exhaust gas system (5) of an internal combustion engine (1) includes a thermoelectric generator (13) with plural thermoelectric elements (15) that each have a hot side (16) and a cold side (17). A heating channel (18) conducts a heating medium on the hot sides and a cooling channel (19) conducts cooling medium on the cold sides (17). The thermoelectric generator (13), the heating channel (18), and the cooling channel (19) are arranged adjacent in a stacking direction (20) and form a channel stack (21). A housing (8) that encloses an interior (22) accommodates the channel stack (21) and has medium inlets (9, 11), outlets (10, 12) and electrical connections (14). The thermoelectric elements are arranged in a double-walled intermediate bottom (15) that separates the cooling channel (19) from the heating channel (18), adjacent to said cooling channel, in regard to fluid flow.