I did something similar to my 5.7
I figured thsat since outside air is always cooler than air already inside the engine compartment, it just seemed like the easy 'just gotta do it' kind of mod. The biggest difference between our 2 home made versions is that I retained the factory filter and housing.
I used 4" flexible ducting (it looks like dryer vent stuff but is industrial) to route from that same hole under the airbox down & out through that front angled air diverter thing (that I removed), and the open end is right behind the front lower fascia opening.
I used a few layers of weatherstripping foam w/ adhesive backing on the underside of the airbox and another on the metal fender area to ensure a good seal, essentially forcing cooler air to come in through the 4" ducting.
I don't care about water issues because by retaining the factory airbox & filter, it can't get in now any easier than before the mod.
I made sure not to seal off the small drain hole on the airbox, just in case I decide to forage a small stream to make a wicked getaway.
Mine might work better than without the tube, who knows?
Yours probably does, and it looks good too -- you can't eve see mine.