Reddit mentions of Design Engineering 010408 Cool-Tape Self-Adhesive Heat Reflective Tape, 1.5" x 15' Roll

You're saying you're missing the hose that runs to the airbox?

Photos would help

Also, good catch on the heat being an issue.

Mine had a crack from heat, and I noticed dirt/oil under the area it covers. Also had petcock problems, so in trying to seal up the bike completely (decel popping from slip/stock header as well) I patched it up with Permatex Ultra Black, then put some high heat reflective tape over the bottom of it, then used a bit more Permatex to cover up the silver tape for good measure/cosmetics.

The oil return tank (technical microfiche name) began to split at the seam from the heat it appears. It also had pitting/slight perforation from what had to be heat on the rounded part that is immediately above the exhaust.

http://i.imgur.com/j3nccBp.jpg

Here's the tape I mention, and there are dozens of similar products out there.

http://www.amazon.com/DEI-010408-1-375-Cool-Tape/dp/B000E283S0/ref=pd_ybh_10

looks great, maybe some DEI heat tape in either silver or gold for your air box? It will reflect the heat from your engine bay from heat soaking your air filter as fast. I use it for my supercharged camaro.

http://forums.nasioc.com/forums/showthread.php?t=2416797

I use the silver just because of color preference, I hear the gold works a little better.

silver
https://www.amazon.com/DEI-010408-1-5-Cool-Tape/dp/B000E283S0/ref=sr_1_1?ie=UTF8&qid=1478118525&sr=8-1&keywords=dei+tape

gold
https://www.amazon.com/010396-Reflect-GOLD-Tape-Roll/dp/B0039Z5TYU/ref=sr_1_2?ie=UTF8&qid=1478118525&sr=8-2&keywords=dei+tape

It's cool that DEI has a kit specific for the 4.0L engines but to be honest you can do the same thing for a little less than their cost.

DEI 010403 0.75" Aluminized Sleeving Heat Sheath

DEI 010408 1.5" Cool Tape

Does your XJ already have the heat shield installed? If not you can get it here. CBXCB060 SHIELD-EXHAUST MANIFOLD

IMO hood vents are the last thing you should be doing to address heat issues. It's a band-aid instead of finding/fixing whatever the problem is that's causing the heat issues (whether it's heat soak, overheating, etc).

I have a soft sided cooler with a removable hard insert. It's not the best at keeping ice frozen even with the lid shut. Could some kind of tape like this help keep the summer heat out?

https://www.amazon.com/010408-Cool-Tape-Self-Adhesive-Heat-Reflective/dp/B000E283S0?tag=operasport-20

The plan would be wrap the hard insert with this.