turbocharged air is going to be way hotter than intake air.
if intake air is 50deg (because you have a pod in an engine bay) then figure after the turbo its going to be higher, even if its only 80deg, its still higher
in regards to pressuresed air, yes it will move faster, but you are overlooking the fact that pressureised air means that there is more particles of air in a given fixed volume. althought it is moving faster, how do you know that it is cooling twice as much? how do you know that its is cooling proportional to normal air? saying its "close" isn't good enough i believe
its just not as simple as it seems in terms of the physics of it all
now an ECU tune changes the game altogether and its great because the tunes doesn't have to know the slightest of any physics of it all, they simply have to look at the exhaust AFRs and adjust the mixture accordingly..