Due to the lack of sufficient auxiliary electrical energy to drive pumps or fans, the cooling of autarkic thermoelectric systems is confined to the natural convection mechanism. This is regarded as a key weakness and inhibits an adequate overall thermoelectric system performance. In order to enhance the performance of thermoelectric generators (TEG) for powering small consumer units like self-sufficient wireless sensor nodes (WSN), this paper presents a heat exchanger concept to improve the cooling of the TEG. The concept comes without any auxiliary energy and is based on utilizing the chimney effect to improve the cooling rate of a simple fin heat exchanger. With this concept it is experimentally proven, that the electrical output power of a TEG can be enhanced up to 46,2% compared to the conventional passive cooling method with a finned heat exchanger. Furthermore, this paper presents a CFD simulation to reveal further design optimization potential for the proposed heat exchanger apparatus.