I don’t think the reactor would be scrapped, just shutdown for maintenance.
So most of the heat will have to be extracted from a radioactive material, with similar precautions like in fission reactors, where the heat is extracted from the radioactive nuclear fuel.
I am very skeptical that fusion of deuterium with tritium or of deuterium with deuterium will ever produce "clean energy", even if they are the easiest fusion reactions, due to the relatively low temperatures required for them.
It still remains to be proven whether the radioactive waste for a fusion reactor of the kinds attempted now will be less than for a fission reactor.
I wonder, how can this possibly be even a question? Fission based reactors obviously have the same or worse problem of irradiating the entire reactor enclosure and everything around it, so that's at best the same as a fusion reactor + they produce tonnes of very highly radioactive waste that will be radioactive for millennia.
Materials activated through neutron bombardment aren't radioactive for anywhere near as long. And to add to that, nearly all elements produced in a fission reactor are highly toxic in addition to being radioactive - in a fusion reactor if your steel containment chamber becomes activated, you just have radioactive steel, not one of the many many dangerous heavy metals produced through fission.
LFTR would be far better. Neutrons breed new fuel, and it consumes virtually all the radioactive fuel with "waste" that rapidly becomes non-dangerous within a month.
So I would guess neutron degradation of the equipment/vessel/reactor will probably be a similar problem in both cases.
IIRC people have stated that the breeding could also reprocess the bad millenial-scale waste from LWR into usable fuel or other isotopes in MSRs, although maybe not in LFTR.
If we had a decent LFTR industry, we could probably have more specialized MSRs to deal with the "legacy" waste and breeder reprocess into new fuel or other stuff.
The chemists from ORNL seemed pretty amazing. They had all the work done for separating out the byproducts for use in other applications.
The reaction itself kicks off a huge amount of neutron radiation, which eventually makes the reactor chamber radioactive - that is the only radioactive waste that will have to be disposed safely eventually. But neither the fuel nor the resulting product are radioactive.