the enabling signal is activated has exceeded the period of time indicated by counter threshold value zsw then the filtered efficiency change u03b4 u03b7 cooler u2014 filtered which is supplied to debouncing unit 14 is applied as a debounced efficiency change u03b4 u03b7 cooler u2014 debounced to an additional comparator unit 16 in the additional comparison unit 16 the debounced efficiency change is compared to an efficiency change threshold value wgds and an error is determined if the efficiency change is greater than efficiency change threshold value wgds this establishes that the efficiency of egr cooler 8 has changed by more than a certain amount whereby a defect of egr cooler 8 may be detected to implement an engine control system a specification about the exhaust gas recirculation rate egr rate is normally required since the egr rate however depends heavily on the temperature of the recirculated exhaust gas a specification about the current temperature t egr of the recirculated exhaust gas must be provided the behavior of temperature detector 9 however is slow and hence not suited for this purpose example embodiments of the present invention therefore provide for the temperature t egr of the recirculated exhaust gas to be derived from the exhaust gas temperature and the efficiency of egr cooler 8 at a certain mass flow since the efficiency u03b7 cooler of egr cooler 8 may change during the life of engine system 1 it is sensible to adapt the cooler model for modeling the temperature t egr of.