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They tried to keep him warm with blankets and spare clothes... but maybe a fire at that point could have been enough to save him
With hypothermia the body draws the blood in to keep the vital organs going at the sacrifice of the arms and legs. If you heat someone up to quick by using a fire, the blood can rush out from the core and kill them faster. You have to heat them slowly and sometimes getting inside a blanket with them is the best way. Others here with more medical knowledge can explain this better than me and fill in some of the gaps.