"IF" you're talking about with the forge, I'd NEVER even consider running a forge in a basement - just not enough ventilation for a forge.are you heat treaters at home inside or outside?
any in a house/basement?
or only outside/garage/barns/etc with tall ceilings?
OTOH, if you're talking about with an oven - no problem at all in the basement.
If you had a really good vent hood to put the forge under to pull the nasty CO and stuff outside it might be ok.