Hypothermia has to do with conditioning and fatigue as well as temperature. Feed up with warm food before going in. Monitor your fatigue level - quit and get out before you're tired. Be prepared to do a comfortable bivuoac and do it before you're tired, leave energy for cooking, and have the necessary gear. Warm food is a lifesaver. Once they've downed game, hunters are committed, meaning there's work that has to be done before you go home. This doesn't fit with poor conditioning.
If you go hypthermic, you're incredibly weak, mentally fogged or worse. You must have heat, either from hot food or warm surroundings - your body is already at the point where it can't generate heat on its own. You'll die if you don't get heat, and if you're fully hypothermic, you can't do it alone. Turn back or camp while you're still feeling good. High altitude mountaineers sustain hypothermic conditions as a matter of course; many can't force themselves to eat at the extremity, the ones who live manage to heat and drink 4 liters of warm water a day. They are well equipped for clothes, but are usually at the environmental limit of their clothes. They survive, those who do, through good judgement and good conditioning. Some shelter, a stove, some fuel, a couple cans of chili and most importantly some foresight can save your life. Don't forget the matches - disasters have happened because someone who direly needs matches forgot his. Don't hesitate to eat cold food if you can't warm it.