This gas cooling device (20) is provided with: a second heat exchanger (22) supplied with gas from a heater (10), the second heat exchanger (22) cooling the gas; and a first heat exchanger (21) for lowering the relative humidity of the gas cooled by the second heat exchanger (22). The first heat exchanger (21), utilizing heat emitted by the heater (10) or the second heat exchanger (22) during operation, heats the combustion exhaust gases cooled by the second heat exchanger (22).