It could be the same. I always learned the explanation as: 1. Cool to freezing via evaporation. Because this goes as T^4, the time difference is negligible to

It could be the same. I always learned the explanation as: 1. Cool to freezing via evaporation. Because this goes as T^4, the time difference is negligible to reach 0°C. But...hot water loses more volume. 2. Freeze, bit now you need less energy to freeze less material. I did this at home, and the simple check worked: volume was lower in the frozen hot water. This explanation might be wrong! But it works out in simple tests and mathematically.