Earlier quoted context omitted.
You do what you would on a terrestrial reactor, and shut down the reactor e.g. by using control rods, or pulling out fuel rods to shut down the chain reaction. These wouldn't be simple radiothermal devices, but proper actively managed reactor cores. Having said that you absolutely would need active cooling even in a 'shut down' state, probably by circulating a cooling fluid to radiator fins. You might use the same fl…
Absolutely not, in space you have the option of jettisoning the core, carrying coolant for a controlled shut down is a waste of weight. You might even go as far as having 4 disposable cores, one for each acceleration stage.
Additional nuclear fuel, unlike the popular belief says, will not be taking any much significant weight. A critical mass of plutonium is only 10kg, and you will likely have it reduced with moderation and reflectors.
If you have to keep disposing heat away from a powered down, but still residually active core, you will have to keep a no joke mass of radiators just for that.