The invention is directed toward a device for controlling an internal combustion engine. An aspect of the invention is determining a polytropic exponent according to at least two measured values of the pressure in a combustion chamber of a cylinder of an internal combustion engine during the working stroke of the cylinder once an air/fuel mixture of a cylinder has been burned and before the gas discharge valve is opened. A first exhaust gas temperature is determined and a second temperature of the exhaust gas is determined in accordance with the first exhaust gas temperature. The pressure associated in the combustion chamber, the pressure prevailing in the combustion chamber after closing the gas discharge valve, and the polytropic exponent are determined. An actuation signal for controlling an actuating member of the internal combustion engine is generated according to the second temperature of the exhaust gas.