Under ordinary driving conditions, the computer is in closed loop mode and using O2 sensor feed back, it keeps the mixture close to 14.7:1 regardless of the intake air temp. The throttle is in full control of the power being produced by the engine, because it controls the amount of air getting into the engine.
Under wide open throttle (WOT), computer in open loop mode, the throttle can no longer control the power and cooler air can make a some difference in power production. The computer still monitors the intake air temp with the IAT sensor. It knows that cooler air is more dense and so it injects the additional fuel needed to match the denser cooler air. More power will be produced by burning the additional fuel. Obviously, no cool air intake can reduce the intake air temp lower that the outside temp.
Keep in mind the the effectiveness of the intake depends on WOT operation, that is, the accelerator pedal is on the floor. With normal part throttle operation the cool air intake is worthless.
2001 WJ Limited with Quadra-Drive, Kenne Bell Supercharger, 3-inch Kolak exhaust, Stillen rotors (F/R) and MM pads, Addco sway bars (F/R).