There's a lot of heat energy in the evaporated water that makes up sensible perspiration (sweating) and insensible perspiration (which happens continously from our skin).

If you can trap that evaporated water, you create a warm, moist envelope around yourself. That's why some hardcore outdoorspeople put sealed vapour barriers inside their sleeping bags to get more warmth for less weight.

But unless you have insulation outside of the vapour barrier, that warmth would be very short term. The determining factor would be your activity level. If you slow down, after your clothes have become saturated with moisture, convection and conduction would catch up with you. And then you would be really cold.

The Tyvek suit is a good example; the same would apply to oft-repeated advice of "crawl into an oversize trash bag and you'll be fine." I'd hate to spend a night like that; without additional insulation, it would be miserable.

The vest under discussion is a bit different, in that the air chambers won't contain moisture except that from your breath while inflating. If the wearer is moderately active, it will reflect and retain some warmth, though convection losses will be much more than an insulated garment. I think the most effective use would still be to wear it next to the skin, and put any other clothing over top.