A catalytic converter has a carrier structure and a catalytically active coating adhering to the carrier structure, and is disposed downstream of an internal combustion engine of a motor vehicle for cleaning exhaust gas. A method for functional monitoring of the catalytic converter includes determining a temperature of the catalytically active coating and/or of the structure of the catalytic converter at least at one location. A temperature of the exhaust gas is determined upstream of the at least one location of the catalytic converter. At least first derivatives over time of both temperature values are formed. A difference of the derivatives over time is formed. An instant after a start of the engine at which the difference changes its sign is ascertained. An apparatus for functional monitoring of the catalytic converter includes at least one measuring sensor for measuring a temperature of the carrier structure and/or of the catalytically active coating. At least one device determines an exhaust gas temperature. A differentiation circuit forms derivatives over time of the measured or determined temperatures. A subtraction circuit forms a difference between the two derivatives over time. A comparison circuit ascertains an instant at which the difference changes its sign.