A furnace is the most generic term:
: an enclosed structure in which heat is produced (as for heating a house or for reducing ore)
A kiln narrows the uses to which the heat is put:
A forge narrows the thing being heated to a metal:: an oven, furnace, or heated enclosure used for processing a substance by burning, firing, or drying
: a furnace or a shop with its furnace where metal is heated and wrought
So while most of the things I discuss here could use any of these terms, I'll try to use the term furnace generally. Of course the dictionary only records the current meaning of things, so older texts may contradict.