As someone who has fought wildfire before, I personally found that sweat does not accumulate in front of a source of heat. You start to feel damp or wet after you walk away from the heat. Perhaps it is the same with a hot furnace.

I think he's probably sweating, but the sweat evaporates faster than it can bead up. Or maybe he's dehydrated.. I have wondered what the "behind the scenes" of his videos looks like; when he goes out into the woods does he bring modern water bottles and pack a lunch?

hot, dry air has a tendency to evaporate water.