I stumbled across a method for cooking meat that requires only an Igloo-type cooler, a meat thermometer, a Zip-Lock bag and hot water. It's ridiculously simple and cooks meat PERFECTLY, evenly done from edge to center. I claim absolutely no authorship, as I found it Here.
I can say with certainty it works with steak (making a mediocre sirloin fork-tender), pork roast (takes longer, but wonderful) and fish, but there's no reason it won't handle any dead varmint. If you try it once you'll use it again.