Ascoli65 wrote: "Rothwell rightly cited the Newton's law of cooling, but he applied it to the wrong element: the cooling water, the only element of the fat-cat, of which the values of the measured temperature were disclosed. In reality, he should have applied this law to the inner 'hot core' . . ."
This does not make sense.
1. The hot core cannot be much hotter than the metal box (the outside metal), because it is bolted to it, and metal conducts heat well. There is no insulating material between the core and the metal box. The metal box surface was not all that hot. It was not incandescent. It was no hotter in the afternoon than the morning.
2. The core is surrounded by water, which conducts heat extremely well. The core cannot get very hot.
3. As I said, the core and the box are made of iron (steel), which has heat capacity one-tenth that of water. Compared to the water, the iron core and box store little heat.
4. When the power was cut the first several times, the box and water began cooling immediately. They cooled quickly and the curve fit Newton's law of cooling. That was the combined cooling of the water and iron core and iron box. Hours later, that afternoon, the box and water remained hot after the power was cut off, and then cooled slowly. Why would the cooling curve change hours later, unless there was an extra source of heat? There was no physical change in the configuration. The core could not have been much hotter that it was before. The box surface was not hotter that it was in the morning, and was still bolted to the inner core. The core could not have stored any more heat than it did in the morning. The heat transfer to the water and the box walls was the same.
5. In short, the "inner hot core" would transfer heat that afternoon the same way it did in the morning.
Note that elsewhere I said that incandescent iron dunked in water cools instantly. I did not mean in a millisecond. I meant there is a fssssst! sound, a little water boils, and in a second or two the incandescent orange light goes away. Of course the iron is still hot.