The timing on this thread is perfect. I can add some light to these two questions. So a couple of months ago, I went Coyote Flats in the Eastern Sierras. We ended up around 10,000 feet. When we went the weather was cold (probably around 50 during the day and down to 25 at night). While on a slow/long/steep ascend my coolant temp started rising and my AT light came on. So I pulled over and gave the car a break. Later on while stationary after some slow 4low stuff, again it started climbing.
I had serviced the cooling system so I was a bit surprised. It never happened to me on the streets. But something I'd notice occasionally was stains on the expansion tank...meaning some fluid and over flowed. After my trip, I had the mechanic go through the cooling system. The issue was the thermostat. It was "sticking." But they only figured this out by removing it and testing in hot water. After changing it, I went on another trip with a lot of climbing in 85+ weather. No a single cooling issue. In my case I knew the radiator was good, it had been flushed, cracked fan replaced and coolant drained. So not hard to figure that one out.
With respect to the AT light, my educated guess is this: at higher elevation while off roading and very slow speeds, if you leave the car in drive it will usually use a higher gear than it should. This results in more torque converter slippage (by design) which generates heat. Instead if you deliberately use 1st and 2nd gear, then slippage is eliminated which reduces heat. On trips where I've done this, I had zero issues.