Any air compressed beyond atmospheric pressure is heated in relation to the temperature before compression.
Most of the intake air change temperature increase on a turbo car comes from Charles' Law (-edit: and Boyles law) , not because the turbine is physically connected to the compressor.
Under load, touch a Vortech head unit, and a turbo compressor unit and tell me if there is a significant difference in temp between the 2.
There is, Ive seen the read outs on those digital heat sensors that you point at something and displays the temp digitaly. The turbo head unit was much hotter then my head unit on my paxton.
thanks snoozer (<- not sarcasm), i kinda thought some of the exhaust air went through back to the intake side, i did know about the wastegate, i just thought that the hot side was more open to the cold side, and not just a shaft to spin like the supers... so it's all just heat transfer and air compression then, cool