In Wisconsin rifle hunting (in a week) it's usually "refrigerator temperature"... rarely above 50º F. Many times it's below freezing. We gut the deer out right away and lay it on it's belly for the blood to drain. If it's not warm it sits there a few hours. Just get it field dressed asap to let it start cooling down.
If it's unseasonably warm we'll get it into a cooler as soon as we can.