I have no doubt that cooler air gives more power. But moving the intake mouth outside the engine compartment won't change that. If I start a cold engine at zero degrees, and drive it two hours in zero degrees the entire intake plenum will be zero degrees when I stop. Even the oil filler cap is cool. At 6000 rpm, the fan moves 1500 liters PER SECOND of air. Fifteen minutes after shutoff, everything's warm.
There is another reason why you might move that mouth outside the engine compartment. With the fan moving all that air into the engine, there must be negative air pressure in there.
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'83 SC
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