I once checked my temp coming out of the cooler but don't remember the number anymore. I would bet mine might actually coast a little higher...I typically preheat the cooler (not required) and use towels for an hour or so. Just my routine not really needed though.
If you let the butt cool too much they tend to become difficult to pull. If you are pulling after cooking, let it cool until you can touch it without getting burned. Don't let it cool too long, keep it above 140 for food safety reasons.
In Phoenix, we call these Driving Gloves... http://www.allsafetyproducts.biz/sit...%20RAD64057009
I've seen some teams wearing these during pulling. Just the thin Latex or vinyl gloves helps, these rubber coated gloves really keep the working surfaces of your hands away from heat.