Please do your research on this. You want the heat on as low as possible in case of a failure until you are ready for ascent. If you have a heat failure and you've had it on so you are nice and toasty in the beginning you're going to bend yourself like a pretzel. You are increasing the rate of inert gas uptake by being warm at the beginning, and if it fails, you are slowing the rate on the way out. The algorithms are based on the assumption that the rates are not changed by any thermal factors, only pressure changes so they can't factor in your temperature. If you take it in faster and the vest fails, you really need to drop your GF-Hi way down to make sure you get rid of all the gas. What @michael-fisch experienced is getting too hot too late and his body trying to dump it all out too fast which is why it's important that you turn it on/up as you are getting ready to leave the bottom. On a wreck that would be on your way back to the ascent line, on a cave it's a little easier to sort out. If you leave the battery on deco if you're in a cave, then it's important to ease into it and not just slam the heat on.
what's the reasoning for being warmer = higher inert gas uptake? Just from a purely chemistry point of view, gases are much more soluble in cold water than in warm water. I would think you want to be warm to slow your initial uptake of gas. While of course it is more complex, see this chart for nitrogen solubility in water as a function of temperature:
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Coming up, it's much more complex. If you go from cold > hot, you're tissues lose their ability to hold gas, and thus are going to start off-gassing faster. Assuming your tissues don't become supersaturated, that's probably a good thing, as you'll get the gases out sooner. If you lose your heated suits, it might take longer than expected to achieve complete off-gassing.
It seems most reasonable that you want to be warm, and keep yourself warm for the whole dive. That would keep your tissues in a state where they can absorb the least amount of gas, and off-gas at the quickest rate.
I'm not a tech diver (just a chemistry professor), so maybe someone can find a whole in my reasoning, but I think the topic is interesting.
Watch the two videos in the post quoted. I believe it has to do with circulation when the body is hot and cold.