TXnMA already mentioned that even a perfectly functioning, shiny new reactor has lots of ways to produce heat when you don't want it.
But those two (at least) reactors are anything but new. They are junk by now. This means that the fuel rods are partially gone, and the fuel inside was free to fall out and mix with other fuel at the bottom of the reactor. There are no means of controlling the reaction there; temperatures there can be very high, and the resulting mix can burn through anything, considering that it makes its own energy as it goes, and it has a lot of that energy. If such a situation occurs, you will have a few hundred MEGAwatts (up to 600 MW after all fuel rods are gone) produced under the reactor and not cooled in any way. The temperature will rise forever, until the new balance is reached. That could be at stellar levels. No containment vessel can hold this for long - not without corresponding 600 MW of cooling. And that they couldn't adequately do yesterday, in part because the heat-producing area (as I understand) is not accessible. They poured an ocean of water there, and the reactor won - it has unlimited supply of energy in its fuel, and the fuel so far can't escape the containment vessel. Perhaps we'd be better off when the containment fails because under the reactor they have an area that is far better suited for separating and individually encapsulating drops of fuel. But I'm not a nuclear engineer anyway, what do I know...
The plants after a cold shutdown have residual energy of about a third of a megawatt, from nuclear decay only.
That’s simply not sufficient to make the core turn critical.
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I don't recall saying that!
What I did say was that, after a reactor has operated for a while, it accumulates reaction products (in the fuel rods) that, due to radioactive decay, continue to produce heat -- even after the fission reaction is shut down.
The good news (in this case) is that their thermal output decreases exponentially as a function of their half-life. (See jwalsh07's graph above in #311.)
The bad news is that, even after ten days, that radionuclide decay heat output is still significant enough to require supplemental cooling.
Your wild runaway scenario is more bunk than Hanoi Jane in the China Syndome. For one thing, the boron that has been dumped into the reactors will "poision" the reaction to prevent re-start of fission. (That's why new designs also include a boron "catch bowl" beneath the containment vessel....)
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"Stellar levels" -- from a small fission reaction? Talk about "Drama llamas"! Time for you to go to bed -- and when you wake up tomorrow, I recommend signing up for a course in high school physics -- and a Valium prescription...
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"But I'm not a nuclear engineer anyway, what do I know..."
First question you should have asked... '-)