Method for estimating the temperature of a catalytic converter for treating the exhaust gas of an internal combustion engine

According to this method, a) is estimated by iterative calculations the current temperature TG (i) a heater (3) of the exhaust gas according to the energy supplied thereto, the capacity heat of the member (3), a convective heat exchange between the body (3) and the exhaust gas, and b) it is estimated by iterative calculations the current temperature TC (i) of the catalytic converter (5 ), depending on the current temperature of the member (3), the heat capacity of the pot (5), a convective heat exchange between the pot (5) and the exhaust gas, and energy released in the pot (5) by oxidation reactions of pollutant chemical species contained in said exhaust gases.