That depends which one. An open-cone filter with no protection from the heat of the engine bay will just suck in hot air at lower speeds, which in turn will cause the engine to bog down. Acceleration and throttle response will suffer because of this.
At higher speeds it will improve when there is a good, cold, dense rush of air coming into the engine bay, but it wont be much different to stock.
If you get a decent heat shield things get better. Heat soak is lessened and pick up is better because of that... but you'll still be sucking in hot air.
Add a good cold air feed to the mix and things get better still. Some nice, wide tubing taken from lower down on the front bumper will ensure you get a good dose of cold, dense air hitting the air filter which improves everything.
And finally, an enclosed induction kit - like the BMC CDA - will stop heat soak further as it's an enclosed design and the filter itself isn't sucking in hot air as much. With the cold air feed I just mentioned you'll gain a little in pick up and throttle response and possibly 1-2 bhp but that's about it.
HTH