It's funny how nuclear power station meltdowns come to mind before hospitals and building heating.
Anyway nuclear plants undergo quite a bit of study and protection against these kinds of events (solar or military/terrorist EMP) and are expected to just shut down safely.
[1] https://public-blog.nrc-gateway.gov/2016/07/05/update-keepin...
[2] https://www.utilitydive.com/news/epri-threat-of-emp-attacks-...
[3] https://www.forbes.com/sites/jamesconca/2019/01/03/can-nucle...