Abstract: The system for continuous thermal combustion of matter, such as waste matter, is provided with an incinerator comprising an inlet, an outlet and a combustion path extending between the inlet and the outlet. The system further comprises air supply means for supplying heated air to the combustion path. The system is further provided with regulating means for automatically regulating the magnitude of the air supply and/or the temperature of the air supplied with the aid of the air supply means, depending on the heating value of the matter (the amount of heat which is generated upon combustion of the matter in the incinerator).