Should supercharged engines be given extra idle time after being driven to "cool off"?

Probably wouldn't hurt, but in my book it is probably a waste of time and gas as a supercharger is not like a turbo.
A turbo engine should be given a minute or so to cool down/spool down if it'* been driven hard since the turbo is exhaust driven and if really spooled up and shut down shortly thereafter it will still be spinning, but without oil being fed to it.
Superchargers are belt driven so when the belt stops the rotors stop (they better).

Come to think of it now, it probably is almost best to shut it off asap so as not to induce to much heat soak, as sitting idling the engine will tend to heat up (no air being pushed through the rad to cool unless cooling fan(*) are on).

My numbers are a little extreme with the pulley size I'm running now, but let'* use idle as an example.

At idle, the SC wants to run 120-140. Your coolant is what, at least 185? The coolant will heat it up at idle. Under load/use/abuse, the SC temps can spike to well over 200, but the coolant can only cool it later to the coolant temp, whatever that may be. The coolant WILL cool it down to a point, but not beyond that.

The SC is aluminum and has cooling fins (small, but they're there). I'd shut it down and pop the hood for a few minutes if you're concerned. Or install hood vents. Also consider a high-speed fan override. Many of us have.

I see. Ryan has my fans programmed to match my 180 thermostat and they come on much earlier instead of the 230 or so they're usually at.

Thank you. It sounds like it'* not a concern.