What? I bet it doesn't. There's no way cooling will interfere with the half-life of the elements. They probably mean that solidifying the extremities reduces toxic/radiation exposure.
For instance, cooling it will make the molten metals harden, meaning that there will no material transport. So once some piece of the sludge goes out of criticality, cooling ensures that it will stay sub-critical and decay along a more preferable path.
There is also the possibility that water will do something funky to the chemistry beyond the cooling.
Wow, so even at absolute zero, decay happens at the same rate? It kind of makes sense, but it's surprising if you've never thought about it.
Wikipedia seems to confirm it: "A number of experiments have found that decay rates of other modes of artificial and naturally occurring radioisotopes are, to a high degree of precision, unaffected by external conditions such as temperature, pressure, the chemical environment, and electric, magnetic, or gravitational fields." ( https://en.wikipedia.org/wiki/Radioactive_decay )
Beryllium-7 decays purely by electron capture with a half-life of somewhat over 50 days. Differences in chemical environment can alter the half-life by around 0.2%, and high pressures produce somewhat similar changes.
A much more spectacular alteration is if you strip away all the electrons from the very weak beta-emitter rhenium-187 in a particle accelerator, to form a bare nucleus. Neutral rhenium-187 has a half-life of 42 × 10^9 years, the fully ionised rhenium-187 has a half life of just 33 years - a billion fold speed up in decay rate!
You'll never get to absolute zero (reality and practicalness aside), because the element radiates it's own heat.
See the GP, this has been tested and proved to have no effect.
Their big point about dating methods was that radioactive decay could be influenced by external factors. No matter how slight that influence, a tiny little bit was enough to disprove all our dating methods.
Hydrates contain hydrogen, which is a neutron moderator. To the extent that corium's complex decay involves neutrons, changing the neutron energy spectrum (what a moderator does) could change the decay pathways and durations.
Electronic ("normal") and nuclear chemistries can interact.
Edit: Also, water dumped on hot stuff can crack it. Cracks mean that regions of material have changed their geometric relationships, which affect nuclear decay.
Because we already use water based neutron moderators. https://en.wikipedia.org/wiki/Neutron_moderator