His skin would still be warm, blood is flowing through his skin but not to his brain. The vascular system is not one simple looped circuit, each bit linked to the previous and the next.
Its a branched system, and the brain has its own loop with multiple branches off it.
Cutting off the blood supply where it typically occurs with a hanging, you cut off the supply to the brain, but not to the skin.
Just like any other body part really, swelling can cut circulation, but unlike other body parts, the brain cannot swell much before this happens and the pressure would need to be relieved (if thats even possible) by making holes in the skull, letting blood out if there is a haematoma, putting in shunts etc... AFAIK and, I am not a doctor, you can't relieve the pressure of a swollen, coning brainstem, you support the body and either it stops or.. it doesn't.
Again like any other body part, stop circulation and oxygenation long enough and the tissue dies and it wouldn't matter if you could pump blood through it again, it wouldn't 'live' - This is why theres such a short timeframe for transplants or re-attachment of severed limbs (And that tissue has to be in peak condition to start with!).