I dont wrap it, I just put it in a big pan and cover the top.
When you do it old school the way I do, you can dry it out a little if you leave it in there the whole time. Also, it gets more smoke flavor when you cook with real wood, so you dont need to keep loading wood after the first 4 or 5 hours. Its just easier to finish it in the oven.
I know the electrics are way easier, but I love the entire process of chopping the wood to standing around and checking the fire.
I dont use a thermometer either.
I just hold my hand over the chimney to feel for the right temp.