The boiling pot will never pass through the state where it's uniformly room temperature. We did this in high school, and put 3 thermometers in both buckets. At

The boiling pot will never pass through the state where it's uniformly room temperature. We did this in high school, and put 3 thermometers in both buckets. At the point when the water at the very bottom of the hot bucket reached ~6°C, the top of that bucket was still >60°C. This was in a 30cm tall 10 liter bucket, it really surprised us how strongly the water stratified. The top loses heat fast through evaporation, but the temperature of the water at the top does not fall very fast because the newly-cold water flows rapidly down the sides of the bucket. If you add constant mixing to both buckets, the hot one freezes slower than the room-temperature bucket.