corespotlightd is using lots of CPU and iMac keeps shutting down and restarting

You have control over what Spotlight indexes. By default it wants to index a massive number of file types and attached devices. That can slow performance and cause "High CPU use" flags like you saw.

See:

Prevent Spotlight searches in files on Mac - Apple Support

That may prevent you from having this issue again.

Way 1: Kill the corespotlightd process

Way 2: Restart your Mac

Way 3: Reindex your disks

Way 4: Update macOS

Way 5: Clean reinstall macOS