Why not wood? You can easily build wood fires hot enough to work refined aluminum (all those cans, good for something!), copper (rip out the plumbing and wires en masse, it won't be pure but it'll be close enough), tin, and zinc; with copper, tin, and zinc those you can create bronze and brass. Iron would be out of the question with simply a wood fire, but--assuming other knowledge was intact, of course--you could build a forced-draft charcoal burner which can easily get hot enough to melt down some forms of iron.
When I started thinking about this problem I was expecting it to be a tough one, but I think it's achievable.
Iron and Steel can be worked on a charcoal/wood fire. Maybe it won't be easy, but the scale of malleability is basically linear with temperature. Every 100 degrees and it gets a bit softer.
Metallurgically, this won't necessarily yield the best parts if we can't reach critical temperatures - 1900°F, but even then, there are plenty of forgiving alloys out there, and plenty of metal that can be re-worked without melting it down.
The bigger difficulty in my mind is having all the alloys identified. It is pretty business even with good modern tools.
When I started thinking about this problem I was expecting it to be a tough one, but I think it's achievable.