This system, in which the engine is associated with a turbocharger and with a feed device adapted to implement first and second regeneration strategies depending on different engine operation control parameters to obtain different temperatures in the exhaust line, acquires the temperature in the line, compares it with a safety threshold for the turbocharger turbine so that if the threshold is exceeded while applying the second strategy, the feed device is controlled so that one of the engine operation control parameters is regulated to reduce the temperature, and if it does not drop back below the threshold at the end of a first time period, the feed device is controlled to switch over to the first strategy, and if it still does not drop back below the threshold at the end of a second time period, the feed device is controlled to stop the regeneration strategy.