I don't know that much about warm air intakes but I have read a lot about them...
from all the things I have read the 2 major benefits are introducing heat into the engine for a faster warm up to get to closed loop faster which saves fuel.
Then the other benefit is to potentially reduce pumping losses. Cooler air is more dense and contains more oxygen. More fuel can be added for the given volume which produces more horsepower. This is useful if you want to get every bit of power from an engine while running down a drag strip. However idling at a light or cruising around town you don't need power. Yes you may use less throttle but your pumping losses will increase. It takes fuel to turn the engine, with cooler air it takes more fuel to reach stoichiometric combustion....since you aren't using the power the engine is making most of the power is being used to turn the engine.... ergo pumping losses... you are paying money to move cold air through the engine.
In theory warmer air = less fuel for given volume = throttle open a little more = less pumping losses = more efficient engine = ???more mpg???....
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