Well the true reason you want a cold air intake is because cold air is denser, which would bring more oxygen into the engine, resulting in more power. As for your second question anton, it's a little of both. The bigger the opening that air can be sucked through, the easier it is to bring in more air (usually) and a bigger pipe could then handle more air moving through it.
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2008 Jeep Compass Limited 4x4 (4x4 all the way baby!)