If you look through our FAQ's you will find that I have very strong feelings on hanging the deer of today. First, I don't believe that it's necessary for 95% on the deer in the USA. The only time I would say it might be justified is with deer from the big woods areas of the northern states, otherwise I see no logical reason to hang them for extended periods.
    Second, if a hunter still insists on hanging his deer the only correct and safe way to hang a deer is in the controlled environment of a commercial cooler between 28F - 36F.
    Bacteria thrives between 40F -140F. The conditions you've described are ideal for this growth and you should notice the meat starting to smell and get a wet look within 48 hours or less.
    I would recommend you get it to a processor or cut it yourself ASAP.

Dave

PS. Check the FAQ's for further reasons I don't feel hanging is needed.