CAI and Intercoolers

[mchlmpls]

I have been trying to figure this one out but i cant find anything to help me online, so i figured you guys would be a good group to ask. Now i know that a cold air intake system puts cold air in the engine, which makes more power. Does it also do it with force, like a supercharger, or is the only advantage that the air it sends is colder? Second, i know intercoolers make the air colder so the supercharger works better, but what happens if you use a cold air intake system instead of an intercooler with your supercharger? It would do the same thing, but it would be cheaper since all you need is a new hood with a hood scoop, right? What happens if the intake of an intercooler is actually a CAI hood scoop? Is that... double good? Just to clarify, im not talking about a roots charger, im talking about the ones hidden under the hood (centrifugal mainly). I wasnt sure how much that would change everything so i just thought i would throw it in.

[DartGT66]

When you compress air, it heats up. Of course cooler induction helps, but you are commonly talking about some 200+F with boost without an intercooler anyway. So, intercooling really is the only way to keep the intake charge temperatures reasonable. There are intercoolers for roots style superchargers too, and they make a considerable difference in power.