The factory intake already sources 'cold' air from inside the passenger front fender, there is a plastic vent that channels air from in front of the radiator support. Ambient 'outside' air is going to be colder than the engine compartment temperature, especially at low speeds and city driving. Does that answer your question?
If you have a scan tool or a bluetooth adapter and an android device with "Torque" on it, you can see the inlet air temperature. Measuring with / without the top half of the filter housing will show you what you need to know.
Cut and paste from Banks:
The object is to get the coolest air possible to the engine's intake system. Many engines induct air that has passed through the radiator or over other warm areas of the engine, significantly heating the air and reducing its density. By relocating the air intakes to duct outside air that hasn't been warmed into the engine, density is significantly increased. For example, it is not uncommon for air to increase up to 50º F. passing through the radiator and air conditioning condenser on a late model vehicle. The general rule of thumb is that for every 10º of temperature drop, the density (and oxygen content) increases 1 percent. It's actually more like 1.8 percent. Similarly, power increases by an equal amount. So, in this example, if you can intake air that hasn't been heated, you can gain as much as 5 to 9 percent more power. Happily, the best places to collect cool air are the same places that work for ram air, so you can get the density gains from both pressure and temperature using the same intake ducting.