Timer are very popular for the turbo guys to cool off their engine and turbo after rigorous driving and I heard even for NA cars it's a good habit to let the car idle for like 1/2 to 1 minute before shutting off after rigorous driving or a long commute.

Just wondering what MB use to cool off the supercharger (coolant or engine oil?) and whether it is necessary to let car idle for awhile

 

Superchargers operate at much lower temps than turbos since they aren't driven by exhaust gases. I think Mercedes uses engine oil to lube and cool the supercharger. Idling a turbo car is necessary to cool the bearings to keep them from "coking" themselves. It is not necessary with a supercharger.