Just wanted to toss around some ideas about this that I had, I'm still learning about cars / 3G so if there are concepts I'm missing or something lemme know.
I had an idea a while back (similar to 3GJester in https://www.3geez.com/forum/showthread.php?t=3581) as to what effects putting a water jacket around a CAI would have. I read that thread (a bit lost in the carb talk) but from I take away, any sort of way you are trying to "actively" cool the intake air, you're going to use more (outside) power from somewhere else.
So my thought was to have a custom CAI with a water jacket on it (like a CAI inside a slightly bigger tube and pump water between the two) and have an additional reservoir under the hood for the extra water, and use a small electric aquarium pump. For those in colder temperatures maybe a water/alcohol mix or even coolant? But you'd need to make sure the pump and lines didn't corrode. And design the CAI so you still have your MAF working. I think maybe there are two sides of this coin: reducing the temperature of the air or simply trying to remove the heat. A CO2 or gas barrier might be better at actively cooling the air but who's going to carry an a CO2 tank? Unless you've got nitrous. Water runs into the same problem somewhat as you'd have to keep putting ice or dry ice in the tank if you wanted the intake temps to be significantly lower than ambient. Or could you play around with the diameters of the CAI sections to change the velocity? Make bore it or grind it? I've seen some CAI's with a shield (esp on larger diesel applications) but IMO it doesnt seem like a thin metal box around a CAI will block it from heat that much.