A diagnosis apparatus for diagnosing a catalystic converter of a motor vehicle as to whether the catalyst suffers deterioration by estimating a temperature of the catalyst or that of the exhaust gas in the vicinity of the catalyst on the basis of a plurality of engine parameters to thereby decide deterioration of the catalyst by using as an index the estimated temperature. The apparatus includes a unit for estimating the temperature of the catalyst in a steady state by making use of an engine speed and an engine load which represent typical parameters employed in fuel injection control of the engine. The steady-state temperature facility is realized by storing the engine speeds and the engine loads obtained experimentally in the steady state operation of the engine in the form of a two-dimensional data map. A unit for correcting the estimated temperature of the catalyst in the transient state is provided for correcting the catalyst temperature determined by the steady-state catalyst temperature estimating unit to thereby ensure correct estimation of the catalyst temperature even in the course of operation of the motor vehicle. In the transient temperature estimating unit, non-linear characteristics are each described by combining a plurality of linear characteristics. A unit for estimating the temperature of the catalyst on the basis of the value determined by the steady-state temperature estimating unit and the transient-state temperature estimating unit is provided to decide deterioration of the catalyst.