Based on a recommendation form a member of the Airstream Forums I found this fingertip rope caulk. There is 90 feet of happiness in this box!
Simply peel off the necessary amount of caulk and stick it in place before tightening the screws on the heater. I used 2 rows of caulk per side. It will stick to the trailer or heater surface if pressed a little. That holds it in place long enough to tighten the screws.