I'd so build a Clown Furnace.
It occurs to me that
this should have an affect on the quality of the goods. If you could persuade the craftsman to make the item, and any other dwarf to use the item, it'd have a big effect on everyone else. I sort of imagine a madly twisted (yet effective) sword wielded by a dwarf whose breastplate and other armour has a fearful affect on all enemies...[/tangent]
However, back to the idea, if the magma forge dips a heat-pipe into the cell below (even though no obvious material for this is used in its construction, save for the anvil which is quite plainly on the workshop level[1]), and which stretches up into the furnace-like part of the workshop, then it's vulnerable to building destroyers on the level below (at least knocking off the pipe, rendering the workshop useless[2]).
So instead it must bring magma up in some way (again, no obvious moving parts, but perhaps some sort of capillary action?) which means it needs close-enough magma in the current and traditional style of the workshop. I could see a restrained heat-producing creature also being employed in a specially constructed version of the workshop that effectively relies upon a cage-against-furnace design on the same level, with no need for Z-1 to be intruded[2a], with (frexample) a halter to constrain the dragon with and aim its breath to the required spot. Perhaps something stocks-like for magma men. No idea about magma crabs[3], but stick to just the cage (on top of the base material of the non-magma, non-mundane workshop, and the anvil if a forge) as a component, and I could see it being logical enough. (In DF terms, certainly!)
But that's just my simple thoughts, and probably have a number of failings (on top of those I've already mentioned) that I should see if I spent some more time thinking about it.
[1] Perhaps it's an anvil with a "long foot"? But if it's hot enough to make a new anvil in, how come the extant anvil is safe from the heat... My head quite hurts trying to twist
that particular logic around...
[2] At least temporarily. You'd get a new bit of pipe and lower it through the hole like another keel for one of those small sailboats.
[2a] I can see the argument that being trapped below would also give heat to the layer above, but there must be more to it than merely rising heat from a (sufficiently tall) mass of flame, so directing some possibly coerced creature to concentrate their natural flame attack seems to me more properly applied in a horizontal rather than vertical way.
[3] I've got a fort with zombie magma crabs[4]. Must see if I can capture one, just for the 'lulz'. Let's see, I'm already tapping a magma pipe for my red-hot-fluid needs, so if I made another tapping through a corridor with cage-traps (heat proof mechanisms, definitely, but heat-proof cages as well? I assume it'd only be (fireproof) animal cages for the magma-vermin, and I haven't notice fire-snakes in any of my forts for ages...) and kept the other end enticingly open or start an obsidian industry, maybe some would wander into it... Well, perhaps after I've sorted out some other design issues of the above-ground fortress. They're unlikely to wander away before I get around to it.
[4] Apparently you can get a cream for that.