Could it make the turbo too hot? Yes I know it’s water/oil cooled, but still.
The thing is this: the turbo is engineered to push heat out the exhaust. Heatsoaking the engine bay is arguably harder on the turbo, allowing the heat to enter the engine again and reenter the hotside of the turbo eventually.
Hot side stays a little hotter (which is where they're engineered to take heat) cold side stays lot colder. Engine bay stays cooler. Timing improves. IATs improve. Turbo's ability to turn air into power improves.
Even if it's only a slight benefit, less than a hundred bucks, it's definitely worth a go.
That said, don't get oil on it, otherwise you're making a lantern wick. Don't turn the car off routinely immediately after a balls out run, either (even though the coolant system still runs through the turbo, I think you're probably still better to not do things to aggravate that).
At 13 bucks, if you can do the install, it's almost stupid not to try it. That's crazy cheap. That's definitely on the list of mods over the winter.