Fuel efficient devices and methods for protecting an exhaust system, and components thereof, when the exhaust gas temperature increases excessively are provided. The exhaust gas temperature is estimated in response to an internal resistance of an Air/Fuel ratio sensor element. The estimated temperature is corrected in a transition time based on the exhaust gas flow rate and the engine's operating region. When the exhaust gas temperature reaches an upper limit (Tmax), a delay period is set in response to the change ratio of the exhaust gas temperature. The delay period is based on the margin of time before an exhaust system component reaches the allowable heat resistance temperature Tem. The delay period can be corrected based on the outside air temperature and the vehicle speed. After the delay time has elapsed, a fuel increment is started in order to decrease the exhaust temperature.