That isn’t how a nuclear reactor works.
Even after you shut it down there is what is called decay heat that has to be removed…for a long time.
Right after shutdown from full power the reactor still produces 6%-7% of full heat that has to be removed. This amount decays down to about 1% after 24 hours. But that is still a lot of BTUs.
Cooling water needs to be circulated to remove this heat.
This is one of the key safety improvements in some newer reactor designs, having the ability to circulate cooling water without the need for pumps.
^ This issue was the core reason for the Chernobyl disaster. The plant had backup generators, but they took about a minute or so to reach full power. The Russians wanted to test using the residual heat to generate power for the cooling pumps in the interim.
Turns out, that’s not a good idea.
It was also the core reason for the Fukushima disaster. The backup generators got knocked out by the tsunami.
In numerous conversations we’ve had about nuclear power over the years, someone invariably says “if we just got rid of all the regulations it would be cost effective.” That’s true, but not accounting for every contingency leads to disaster. And disasters are really not cost effective.