As I understand it, a k&n or similar induction kit is usually a freer flowing filter. This allows the air to be drawn in with less resistance, resulting in more flow rate. More air, assuming correct fueling = more power.
The small loss of power associated with the intake of warm air should be outweighed by the extra flow rate/lower resistance of the induction kit.
The standard airbox with it's convoluted entrance tubing etc is designed to baffle the intake noise as well as filter the air. It's sort of like a silencer/exhaust backbox for the incoming air, this means it's not as efficient as it could be at supplying air to the engine because it also has to keep it quiet. Thats why induction kits are louder as its just a filter and not a box
Airbox tuning is very complicated and just whacking on a k&n or similar usually has no or very small benefits on a modern well designed fuel injected car. On the older carby models they could yield big improvements with careful set-up.
Even then the filter/induction kit should be matched to a less restrictive exhaust and altered fuelling. It's best to get the car re-chipped/re-mapped with a fuelling map to suit the new airflow through the motor.
Now, people will say that the bravo has a lambda sensor and will adjust automatically, but they still work off the standard fueling map which may not have enough "range" to cover the mods.
