Right. Yes. I believe I said that here:

    powered by exhaust gasses, which is known as a "turbocharger"

Yes, a lot of energy goes out the exhaust and turbochargers use some of it to compress air for the intake. Even with that there's still energy wasted out the exhaust. If it is hot and makes noise there's energy going out the exhaust. Principle of Conservation of Energy.

At the most basic level thermodynamic machines are about max delta T.