Abstract: A preheated fuel-air mixture is subjected to the following sequential steps: it is ignited, the flame is scanned, the burning mixture is introduced onto the free upper level of a radiation substance charge which is then passed along first heat exchange surfaces, a glowing flameless combustion zone is produced in said charge; beyond said zone the combustion gases are passed along second heat exchange surfaces of an increased area relative to the first heat exchange surfaces, with changed rate of flow. The apparatus is equipped with an ignition and flame scanning gap above said charge and with heat exchange tubes which are divided into several branches past said glowing combustion zone.