An internal combustion engine has at least one cylinder and an exhaust gas tract, in which an exhaust gas sensor, that can be heated in a controlled manner, is arranged. An exhaust gas temperature of an exhaust gas flowing in the exhaust gas tract is determined as a function of the heating power (P_HEAT) supplied to the exhaust gas sensor. An estimated value of the exhaust gas temperature is determined as a function of a physical model of the combustion of the air/fuel mixture and of the exhaust gas tract as a function of at least one operating variable of the internal combustion engine, but independent of the heating power supplied to the exhaust gas sensor. Model parameters of the physical model are adapted as a function of a deviation of the estimated value and of the exhaust gas temperature determined by the supplied heating power.