Method for managing the priming of at least one exhaust gas post-processing device of an internal combustion engine of a motor vehicle, comprising the determination of the minimum number of heating means of said post-processing device to be actuated and of the minimum amplitude of heating by said heating means for the rise in temperature to the priming temperature of said post-processing device , said determination being made as a function of the running profile associated with one or more operating characteristics of the vehicle influencing the rate of heat generated by the engine while running, said method further comprising the determination of a target priming temperature (T° cible ) of the exhaust gas post-processing device, CHARACTERIZED IN THAT it comprises the following successive steps: - the establishment of reference curves representing the contribution of total mass heat from the engine while running, for several running profiles each associated with one or more operating characteristics of the vehicle, according to the following equation: Total mass heat contribution = C p t ∗ ∫ 0 t Qéch m ∗ T entrée t ° − T cible ° dt in which C p is the heat capacity of the exhaust gases; Qéch m is the mass flow rate of the exhaust gases; t is the total running time considered; T° entrée(t) is the temperature at the input of the post-processing device; and T° cible is the target priming temperature of the exhaust gas post-processing device identified; - the determination , for each of the running profiles associated with a reference curve, of the minimum number of heating means to be actuated and of the minimum amplitude of said heating means to reach the target priming temperature T° cible of the exhaust gas post-processing device; - the determination of the internal temperature (T° interne ) of the exhaust gas post-processing device and, when the internal temperature (T° interne ) that is determined is lower than the target priming temperature (T° cible ) , the establishment of a curve of the current situation determining the total mass heat contribution; and - the determination and the setting of the minimum number of heating means and of the minimum amplitude of heating of said heating means, as a function of the comparison of the established total mass contribution curve with respect to the reference curves. - the establishment of reference curves representing the contribution of total mass heat from the engine while running, for several running profiles each associated with one or more operating characteristics of the vehicle, according to the following equation: Total mass heat contribution = C p t ∗ ∫ 0 t Qéch m ∗ T entrée t ° − T cible ° dt in which C p is the heat capacity of the exhaust gases; Qéch m is the mass flow rate of the exhaust gases; t is the total running time considered; T° entrée(t) is the temperature at the input of the post-processing device; and T° cible is the target priming temperature of the exhaust gas post-processing device identified; - the determination , for each of the running profiles associated with a reference curve, of the minimum number of heating means to be actuated and of the minimum amplitude of said heating means to reach the target priming temperature T° cible of the exhaust gas post-processing device; - the determination of the internal temperature (T° interne ) of the exhaust gas post-processing device and, when the internal temperature (T° interne ) that is determined is lower than the target priming temperature (T° cible ) , the establishment of a curve of the current situation determining the total mass heat contribution; and - the determination and the setting of the minimum number of heating means and of the minimum amplitude of heating of said heating means, as a function of the comparison of the established total mass contribution curve with respect to the reference curves. <EOS>