Well you may want to compare how it affects your fuel economy, you may get better economy on cooler days. Alot of car manufacturers tend to put the air feed quite close to the engine, presumably so it warms up quicker. But I've seen a lot of people modify the air intake to get a cold air feed.
The intake is taking air from outside the engine bay, and I have redirected it to take in engine bay air near the exhaust manifold on past cars.
Warm air is less dense, so less of per volume, which means less fuel burned in the cylinder. At least that is the theory, but the only fuel economy benefit could simply be from faster warm times. It does reduce the power output.
Faster warm up
Lower throttle restriction
recycling otherwise lost heat energy
Some cars react well to WAI (warm air intake), others not so much.
Cold dense air is better for power, BUT ONLY TO A POINT. Think 40 below 0 (same temp F or C).
Think 100 degrees. Air density decreases by 25% from the freezing to boiling point of water. Air temp is a useful "displacement reducer" which means more throttle opening for the same power produced = less restriction to intake airflow, lower manifold vacuum.
Take it to the extreme and you could control the intake air flow through temperature alone.
Which is better for economy? Lower manifold vacuum and better atomization is more efficient, particularly in grossly overpowered cars that run normal speeds with high manifold vacuum and lower engine loads.