The turbo is permanently driven by hot exhaust gases at up to 30,000rpm depending on how its vanes are varied. Petrol turbos are almost invariably water cooled by the engine coolant running through them as well as cooled by engine oil running through the turbo bearings. The reason for idling a very hot turbo before switching off is to keep cooling water and oil running through the turbo as it spools down from those very high revs to idle revs and prevent the oil in the bearing and feed pipe to it from carbonising. Some cars (including MINIs) have electric water pumps to keep the coolant flowing after the engine is switched off.