I know everybody has their own experience and opinion, but all the advice I've always recevied about ANY meat is to keep it below 40 degrees if you want to be sure that bacteria will not grow. Bacteria growth not only is potentially dangerous but will also affect the flavor and integrity of the meat/flesh.
If I can't keep the carcass below 40 I process it right away, at least into quarters or smaller, and right into the ice cooler.