Just played after the hotfix, adding coal to the furnace seems to result in it outputting "NaN" heat, so I can't heat up the copper shards to progress
Ran into this same problem. I was able to get past it by manually editing my save and replacing both instances of NaN (forge heat and copper heat) to 0.
how do you manually edit your save file?
The file is a plain JSON object that gets added to %AppData%\LocalLow\The Prismatic Forge\Isekaidle\saves, so you can adjust any values there.