The device has flue gases (22) of a furnace heat source (2), which are fed through the inner and outer gas shaped hollow media space of the a furnace pipe heat exchanger (29). One or multiple pivot bodies, particularly pivoting baffles (37), are arranged spatially behind each other in longitudinal direction in the furnace pipe heat exchanger. The pivot bodies are deviated depending on pivot angle adjustment (24) of a baffle so that the effective surface transversal section increases for unhindered flue gas flow and decreases in reverse direction during the increasing pivot angle degrees. Independent claims are also included for the following; (1) a method for heat transferring of a furnace heat source for heating buildings and for generating hot water by a furnace pipe heat exchanger; and (2) a heating circuit with a media temperature.