The flue gases formed in the combustion chamber of the incinerator furnace, after they have reached a temperature of about 450.degree. C., are brought to a temperature of 200.degree.-250.degree. C. by shock-type cooling. Before this shock-cooling (quenching), heat recovery from the flue gases is carried out in a high-temperature stage from 1000.degree.-1200.degree. C. to about 450.degree. C. and, after the shock-cooling, in a low-temperature stage from 200.degree.-250.degree. C. to about 150.degree. C. As a result, a de novo synthesis is avoided in which dioxins and furans are formed from the components of the flue gases and the fly ash.