First regenerators (3A-3C) which are in combustion exhaust gas exhaust passages, second regenerators (4A-4C) which are in suction/recovery passages for sucking and recovering N2, an atmospheric gas, are provided to three or more regenerative heaters (1A-1C), respectively. In one (1C) of the regenerative heaters (1A-1C), the sucked N2 atmospheric gas is passed through the second regenerator (4C) to regenerate its sensible heat. In another one (1A), combustion air is passed through the second regenerator (4A) in which the heat is stored and combustion is carried out by using the heated air. Only the combustion exhaust gas is passed through the first regenerator (3A) for regeneration. In the other one (1B), the N2 atmospheric gas is passed through the first regenerators (3A-3C) in which heat is regenerated to convert the regenerated heat into sensible heat, which is supplied to the atmosphere of an object and heats the object. These processes, i.e. combustion, atmospheric gas heating and atmospheric gas suction, are repeated in this order. Thus, the atmospheric gas is recovered and reused, and the sensible heat of the atmospheric gas is converted into the sensible heat of the combustion air to improve the heat efficiency.