One thing I learned the hard way is to not be in too much of a hurry to go from smoker to faux cambro. Leave the butts sitting at room temperature until they start to cool a bit. I did two (maybe three?) butts and went straight into the cooler for four or five hours. The cooler was so efficient the butts stayed above 150F the entire time. IOW, they continued to cook. Virtually all the collagen rendered, and, trust me, this is not the good thing it might sound like. Almost all the meat was like mush. It tasted okay but the texture was like baby food.
The thing to remember is there is "resting" and there is "holding". These are different. Resting is when it stops cooking, begins to cool down a bit, and the muscle fibers relax and start to re-absorb some of the juices that were squeezed out. Holding is keeping the rested meat at a safe temperature prior to serving.
I wouldn't be overly concerned about it getting too cold when it's still whole and wrapped. A big piece of meat like that cooked to ~200F is going to stay plenty hot for a long time. I would let it rest at room temp until the internal temp has dropped to 170F or a little less and then move it to whatever you've decided to use for holding.