I came from the turbo world and know minimal about superchargers. In the S4, do i need to let the engine idle for a minute or two after stopping to cool down the supercharger?

I know with turbo'd cars, you should do it to let oil circulate thru the turbo to prevent the oil from burning up inside .

Turbocharger impellers are driven by hot exhaust gases and build a lot of heat. The supercharger rotor(s) are driven by a belt.

So, no motor oil circulates thru the supercharger at all?

There is oil in the supercharger. But I don't know if it is internal to the engine sump or external. But the oil does not see those extreme temps like a turbocharger sees. Here is a great Servie Training manual download of the engine:

http://www.s4-mtm.com/images/925803_3.0V6TFSIengine.pdf

Sweet, thank you!

so can also

Here is a great Service Training manual download of the engine :

That was excellent. I spent the last couple of hours reading.

Just finished reading this and wanted to say thanks for posting it!

To the OP, no, you don't have to let it idle. The car has what's called an "after-run coolant pump" that circulates coolant thru the supercharger intercoolers so they don't overhead from heat soak.

-Jesse