Warm air also makes less power, so why wouldn't that offset any leaning of the mixture that might give better mileage? Why do most all vehicle makers go to the trouble to make cold air intakes, if warm air is better?
There won't be much warm air until the engine actually warms up anyway. The difference in combustion temps due to the difference in intake air temps would be negligible.
I just can't accept this theory, until somebody proves it under scientific test conditions. I know what turning the intake heat on does to an aircraft engine.
As Mack Truck said of their chassis mounted direct air inter cooler, "the cooler we run, the hotter we burn"...
Warm air will give less power but use less fuel. Opposite for cold.
Just look at mileage for summer and winter.
Most airplanes have charts/graphs for fuel consumption at various altitude, power settings, and temperature combinations. And I'm not talking about just large jets here but everything down to home-built kits.
The colder the air,the denser it is so therefore it will take more fuel for any given volume of air. The ratio of air to fuel will be the same but because it's much denser you'll get more power from it. But more gas is used.
The warmer it is.. it'll be less dense. The air/fuel ratio must stay the same so now it'll be less fuel for any given amount of air.. so you'll get less power and burn less fuel.
When you lean the mixture you're changing the air to fuel ratio.. with cars that's generally done automatically for you (open/closed-loop etc) so they can stay as close to a stoichiometric a ratio as possible. That just means the ideal mixture (I think it;s around 20 parts air to 1 part gas).
The difference in my truck,especially in the winter, could be significant. -30 outside and +20 under the hood once the engine gets to operating temp. Mileage could be almost as good as in summer. I usually get about 25% worse mileage between October and April.
I assume the 'intake heat' you mention in an airplane must be carb heat. When you apply carb heat you're supplying the carburator with WARM air from around the engine to get rid of any ice forming in the venturi. Now, when you select that warm air, you usually have to lean the air/fuel ratio because now the engine is running too rich from too much fuel.