To shut down a nuclear reactor you insert neutron absorbing control rods. You do not remove the fuel rods. After the control rods are inserted the fission reaction is quenched but radioactive decay continues to release heat (not at the level of full power output) which necessitates maintaining a flow of cooling water.
That is only one problem, there are "spent" fuel rods, stored on site in a water filled pool. The spent rods are still undergoing radioactive decay and are releasing heat so the pool needs to be kept at level well above the stored rods. The worst release of radioactive material at Fukushima came from the fuel storage pools when the water level dropped below the rods, which melted their casings and released decay products along with some plutonium to the air.
Regards,
GtG
Scram!
I knew that!
;-)
Trouble is, even after an event and a successful scram, as you say the heat continues to build up. Without some kind of intervention, it will eventually start to lose the internal support structures and probably go critical again.