"By taking sumptuous amount of cold air directly to the engine it provides the engine with abundant oxygen. Cold is important too because for a given volume more air will fit in if it is cold and less will fit in if it is hot. This abundant oxygen ensures that the fuel is combusted very well and fuel left unignited due to a lack of oxygen is reduced. The fact that a higher percentage of the fuel is combusted means you get a better fuel efficiency. And the fact that more fuel is burnt in every engine cycle means you get more power. Often extra power is at the cost of lower fuel efficiency but a cold air intake manages to do both."
Cold air intake improves engine life
Cold air=dense air=greater efficiency
This isn't a secret, really.. It's common fact elsewhere, but even simple things become foreign with such fixation on MPGs alone.
Same with cooler engine parts meaning longer life. Does an overheated engine run well? Obviously not. Continuous heating over time has the same effect as one burst of heat. Look at slow cooking versus high heat. They both end up cooked, it's just a matter of when.
All engines have an optimum operating temparature. This is when they're "warmed up." Anything beyond it is less than beneficial.
"Cooling is also needed because high temperatures damage engine materials and lubricants. Internal-combustion engines burn fuel hotter than the melting temperature of engine materials, and hot enough to set fire to lubricants. Engine cooling removes energy fast enough to keep temperatures low so the engine can survive."
http://www.answers.com/topic/engine-cooling