A control apparatus for an internal combustion engine having a means for performing a model calculation to calculate, as an exhaust temperature calculation value, the temperature of exhaust gas in an exhaust branch tube at the time of starting an engine, using a model representing the temperature behavior of the exhaust gas in the exhaust branch tube during stop of an engine; and an exhaust temperature actual measurement value output means for detecting the temperature of exhaust gas in the exhaust branch tube, and outputting the detected temperature as an exhaust temperature actual measurement value, wherein the model includes at least one parameter.