The problem is both highly complex, but fairly easy to model. Engineers have been doing this for over a century.

Of all the cooling modes identified by the author, one will dominate. And it is almost certainly going to have an exponential relationship with time.

Once this mode decays below the next fastest will this new fastest mode will dominate.

All the LLM has to do, then, is give a reasonable estimate for the Q for:

$T = To exp(-Qt)$

This is not too hard to fit if your training set has the internet within itself.

I would have been more interested to see the equations than the plots, but I would have been most interested to see the plots in log space. There, each cooling mode is a straight line.

The data collected, btw, appears to have at least two exponential modes within it.

[The author did not list the temperature dependance of heat capacity, which for pure water is fairly constant]