[ecomodded]

The premise is that the car will make less hp and use less gas.

My deduction could easily be flawed but here it is in a nut shell. Cold air has more explosive potential and hp than warm air when in a compressed cylinder because the air is denser.
The sensors on the car keep the air fuel mixture correct, the colder denser air would need more fuel to stay at the correct level. With warm air the car would lean out the mixture to correct the air fuel mix. As a bonus the warmer air fuel mix ignites a substantial amount easier.