In an exhaust gas processing device wherein in order to efficiently outwardly discharge heat at high temperatures of about 90-150° C. released from a GGH reheater during the shutdown of a desulfurizer, to prevent damage to equipment and corrosion preventive lining material, and to ensure long-term stabilized use of the exhaust gas processing device, at least a GGH heat recovery unit, an absorption tower, a mist eliminator (M/E), and the GGH reheater are placed in a duct for exhaust gases discharged from a fire furnace, in the order named as seen from the upstream side of a flow of exhaust gases, an exhaust gas duct between the M/E and the reheater is provided with a heat radiation device or the like having a heat suppression function for suppressing dissipated heat from the reheater.