That is not true.
Hot water can cool down faster because of the higher difference in temperature.
But by getting cooler the temperature difference decreases and therefore the cooling rate, too.
E.g.: Water at boiling point = 100°C in surroundings of freezing point = 0°C cools down faster from 100°C to 50°C than 50°C to 0°C.
But it still has to take the same time from 50°C to 0°C once it reaches 50°C.
So water from 50°C to 0°C takes X minutes while water from 100°C to 0°C takes X+Y minutes.
It does NOT cool faster to 0° than the 50°C water.
Normally freezing a hot water will take longer than cold, cause freezing "eats" a bunch of energy, and reducing temperature "eats" some too. So the hotter the water the more energy needs to be "eaten" to cool it down towards the freezing point, and then more needs to be eaten to freeze the water.
But there are some conditions where hot water would freeze faster called Mpemba effect.
Wait, isn't the demon lord the girl with the hero who used to be the MC's fiancée? The fact the generals don't know is crazy... unless they were intentionally left in the dark? Doesn't make sense to me, but oh well.