I don't know, but I would be comfortable sticking a thermometer in the thickest part of the meat and leaving it there to see the temp. I would also have a 2nd one just to see the temp within the compartment... with no ice on it of course. LOL!
I know meat at 40°-43° will age deer pretty good for several days. If it's warm out, another way I age deer, is to debone the meat, by removing it from the carcass and place in larger Tupperware containers and place in the refrigerator for several days.
Regardless of what I do, the first thing I do is remove the backstraps and loins inside the body cavity. The rest usually hangs for a few days, unless it's warm, then it gets removed and put in the refrigerator.
iSnipe