A procedure to operate an exhaust gas treatment device, which contains a catalytically active surface for the exothermic conversion of a reagent substance, and a device to implement the procedure are proposed. Provision is made to measure a first measurement for the reaction temperature of the reagent substance in the area of the catalytically active surface as well as to calculate a second measurement for the reaction temperature using a model of the catalytically supported reaction. A measurement for the unconverted reagent substance in the area of the catalytically active surface is ascertained from a comparison of the two measurements. The procedural approach according to the invention makes possible on the one hand a protection of the exhaust gas duct components with regard to an excessive temperature and on the other hand an energy efficient heating of the exhaust gas duct components.