Heat at Air Intake

[littlefarny]

Hi guys, not a whacky idea this time, I promise

Exhaust gasses and intake gasses are normally quite hot due to all of their movement through the various systems they go through (including combustion!), and as density changes at an almost inverse exponential rate against temperature, is it a good thing they're warm?

Sure the increased pressure might be good, but is the decreased density good for combustion?

Would it be possible to pass the exhaust from a turbo for example through a water/oil coolant system to make sure that it doesn't get too hot?

Air in >> Combustion >> Exhaust >> Turbo >> Coolant System >> Air System

Of course there would need to be some regulation to make sure too much kinetic energy isn't robbed, but is this just too much effort for too small a gain? Is it even viable in the first place?

Thoughts please!