NOVELTY - The heat exchanger (1) has a heating channel (2) by which the heat transfer of exhaust gas heat contained in the exhaust gas (9) to the cooling medium is performed. The cooling medium (6) flows through the cooling passage (3). The heating channel is subdivided into a supply chamber (7) and a discharge chamber (8). The discharge chamber is arranged at the heat exchange wall (4) which is directly adjacent to the cooling passage. The supply chamber is arranged on heat exchange wall opposite to discharge chamber. The discharge chamber and supply chamber are extended in parallel.    USE - Heat exchanger arranged on exhaust line of motor vehicle.    ADVANTAGE - The heat exchanger enables higher quantity of heat escape from the exhaust gas. The exhaust gas of the heating channel is discharged through the exhaust gas line, and is exited into the environment according to muffler. The exhaust gas collides against the wall and spreads to the impact area in a star shape on the surface of the heat exchanger wall, so that efficient heat entry from the residual heat contained in the exhaust gas into the heat exchanger wall takes place. The heat exchanger fins increase the surface area of ??the heat exchanger wall and allow better heat transfer of the respective medium in the heat exchanger wall and thus to the respective opposite medium. The high-corrosive portion contained exhaust gas which affects the thermoelectric generator elements can be avoided so that long service life of the thermoelectric generator elements is achieved. The efficient heat transfer from the exhaust gas heat exchanger wall on in the heat exchanger wall takes place, and heat exchanger performance is enhanced. The good thermal conductivity between heat exchanger wall and thermoelectric generator is enabled. The liquid metal permits to compensate for geometrical variations in production, so that full face contact between the thermoelectric generator element and heat exchanger wall is given.    DESCRIPTION OF DRAWING(S) - The drawings show the cross-sectional views of the heat exchanger with thermoelectric generator.    Heat exchanger (1)    Heating channel (2)    Cooling passage (3)    Heat exchange wall (4)    Cooling medium (6)    Supply chamber (7)    Discharge chamber (8)    Exhaust gas (9)