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Cold air contains more oxygen, hot air has less oxygen.
In the tuner world you want a cold air intake so you can inject more gas with that air to gain more power.
With economy, you would want less air, thus less fuel used, and better economy.
Also there is a plus side in that warmed up engines at "operating temps" get better gas mileage, using hot air in the intake warms the engine up quicker, getting you to those better gas mileage conditions faster.
I'm sure there are better explanations with more specifics, but this is the jyst of it.
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