In layman terms, the molecules in hot water are bouncing around more and thus easier to form crystal structures because of the higher-energy state. Molecules at room temperature have to be forced into crystal structures which takes longer.
So, the answer to your question is "a really large number", but it's not obvious that Frozen 2 would have influenced them.
It was always a silly notion, especially when numbers like 30C - a dilution of one part in 10^60, or one molecule of the target substance in 3 × 10^34kg of water, after you understand what molecules are - were being thrown around, but there was at least a plausible explanation before, say, WW1.
If you want a very simple analogy, boiling water is strongly self stirring especially in a cold environment, whereas cold water in a cold environment does not self stir.
This effect is very old popular science filler material, and in the 80s there was possibly a Mr Wizard or similar TV episode where the effect was demonstrated by taking aquarium air tubing and an "empty" mustard squeeze bottle (only worked with one specific brand, plochman's mustard I think) and fill the "empty" mustard bottle such that you've made free yellow food coloring, then stick the aquarium hose in the clear bucket of freezing water and squirt in some mustard food coloring and watch how the convection currents in the previously hot container are huge and the water turns uniformly yellow in seconds whereas the previously cold water the yellow diluted mustard-water just sits there, pretty much. Its easy to use the hose and a stopwatch to try and quantify the currents. Now a days kids would probably use a smartphone camera or ipad and then use a video editing program to quantify the actual water current speeds vs time/location, but its easy to miss the important overall qualitative interpretation by trying too hard to generate too much quantitative information.
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.
In a typical pot, heat is added at the bottom and lost at the top (mostly through evaporation) and a bit at the sides. When heat isn't added anymore energy loss will still be mainly at the top and at the side, at least when not put on a cold surface. When suspended, e.g. on a gas stove, air convection will mage sir that the sides lose now energy than the bottom. So the direction of the convective drive remains the same in the switch from (usually more violent) heating to chilling, so it will sustain relatively well.
On the other hand, while the inertia fades the energy contained in the movement is turned into additional heat that needs to be transported say, but that's a miniscule amount of energy compared to that contained as heat: try to heat up water beyond room temperature by stirring!