Turbo charged engines do not really need to be cooled down and can run a long time without overheating.
However it's best to not immediately shut the engine down after driving hard with the turbo charged engine.
So if you drive the engine hard then you should let the engine idle and cool down for a few minutes before shutting it down completely.
If you just drive the car with the turbo charged engine for a few miles or up to 20 miles or so then you shouldn't have to let the engine idle for a few minutes before shutting down.
But if you have drove the turbo charged car for around 50 to 100 miles or longer then you should let the engine idle for 2 to 3 minutes to allow the engines turbo system to cool down a bit before shutting the engine down.
If you do not let the turbo charger cool down for a few minutes then it can cause damage to the turbo charger.