We have been experimenting with an enclosed box for the filter and providing "ram" air to the box at our shop. See picture below:
We've taken temperature readings on the inside of the box and outside box on a 90+ degree day at idle and highway speeds. The temperature inside the engine away from the filter was much higher (around 190 degrees) and lower at the filter (around 130 degrees) without the box. We added the box and ran another trial and showed that with the enclosed box around the filter and forcing ram air the temp was constant around 100 degrees. That's pretty significant on a warm day this past summer. It is agreeable that the enclosed filter does show a decrease in temp.
Air coming through the grille isn't where fresh air is getting to the filter. It's the hole just below the filter where the factory air box use to sit. We have added a 3" flex hose from the lower air dam and routed it to the bottom of that hole to provide "ram" air so to speak to the filter. Very seldom does the filter area stay the same ambient temperature as the rest of the engine while the car is moving. I hope we all can agree on that statement.