Does anyone actually make an iron that's induction heated without using Curie temp stabilization?
The advantage would be that you can deposit heat in the tip without incurring the temperature drop and time constant that convection/radiation from a heater gets.
Downside is, you need active cooling on the coil to keep it coil...y, otherwise it's going to get at least as hot as the tip, and then you still get the temp drop and time constant, just at a lower order (a pole-zero response I suppose).
Needless to say, coil efficiency drops severely with temperature, because copper has a huge tempco. You might not be able to use copper at all, in which case the efficiency is that much lower to begin with (though the tempco can be lower, so at least the efficiency is flat). And then you're that much closer to the original resistive-heat case, and there's some Q factor where you need to ask, why bother?
(Q factor roughly being in terms of, say, unloaded coil Q, which if it's 1 or 2, isn't much magnetic field, regardless of what you put around it. If it's 10 or 100, it's probably going to be a reasonable fraction due to induction. Presumably your coil coupling will be excellent, so that even a low Q could potentially have quite reasonable efficiency. But if it's 1 or less, even that won't help you.)
As for the power supply, I would assume a variable frequency drive is fine in this case, and that you have a shielded or balanced cable supplying power to the iron. For low Qs, an off-the-shelf resonant controller will do, probably with a transformer to adapt to the coil impedance. (The resonant cap can be onboard, or possibly in the iron if there's room.) For higher Q (more than maybe 5 or so), a slower controller may be desirable, like a PLL+VCO. This may not be as feasible using OTS controllers (that tend to have intentional quirks, which improve regulation or efficiency in traditional topologies like LLC), but a CD4046 or the like, can be used with a little glue logic, to good effect.
If constant frequency is desirable, that's probably fine too, and can even be direct drive (nonresonant) up to modest Q. (The downside to nonresonant is, if you're delivering say 100W at a Q or 10, that's 1kVA the cable, inverter and bypass caps need to handle. They don't know any better, they think you're making 1kW. So they need to be that much higher efficiency, and costs go up very quickly. We're already talking boutique quantity and pricing, so I assume there's a little budget for that, if it should prove useful.)
Tim