[Christ]

Believe it or not, a CAI can have a cooling effect on the engine.

Imagine what happens when you drink cold water. The first process for you to metabolize the water (as if there were such a thing) is for your body to bring that water up to temp. That takes energy, does it not? Some of that energy could have been used as propulsion, rather than wasted as heat in order to bring the air up to temp for combustion.

That's about the easiest way I could explain it.

It is the thermostat's job to open and close to maintain a specific temperature range within the engine, but the coolant's job is to extract heat, not provide or insulate it. The air temp is important in this respect, because colder air will also pull heat away, and since combustion provides heat to the engine, part of the heat that would normally be given to the combustion chamber is then given to the air.