In connection with the desulfurization and dedusting of flue gas where use is made of a combined spray drying and absorption and the material produced by this process is filtered off from the gas stream together with fly ash, a heating of the flue gas is performed prior to its discharge into the atmosphere by admixture of hot, non-purified flue gas. This admixture takes place so that the flue gas serving for the reheating passes through only a part of the available filter area, which allows the remaining part of the filter area to be kept at a relatively low temperature. This results in a particularly high sulfur dioxide absorption being achieved during the passage of the flue gas through the filter.A baghouse unit divided up in a special manner can be used in the process.