"Trimming air box"

True; but if you were using A/C anyway, it would be no extra energy loss. And when you need the A/C is also when the engine needs cooler air more.

I hate to sound rude, but go do a google search on "perpetual motion..."

If you are using the AC, then you want cold air.. if it is being spent on cooling your intake charge, it isnt being spent on cooling YOU. Also, don't forget that all an air conditioning system does is MOVE heat... to the evaporator coil, in front of the radiator.

All that "cooler air intakes" are good for is cramming more air into the engine than would otherwise be done. This is MUCH more readily accomplished by using a turbocharger than by re routing your AC to cool the intake. You're using say, 100 watts of power to add a potential for an extra 5 watts of output from the engine. "Diminishing returns" doesnt even BEGIN to cover it. If this sort of thing made that much of a difference, the automotive engineers would have figured it out before all the modern advancements in forced induction came in.

It just won't work.