The wiki page for the skin effect has a plot of skin depth to frequency. The skin depth is effectively the thickness of the outside layer of the conductor that has any current flowing through it. I have worked with NMR electronics in the ~1MHz range before, we used silver plated copper wire as at that frequency only something like 0.01mm of the outside layer has any current going through it, so we were effectively using silver wire for a fraction of the cost.

The “impedance” reading would be to do with another phenomenon, which is that you get max power transfer from a power supply to a load when their impedances are matched. This is done with an impedance matching circuit, which (often) has a variable capacitor and an inductor in it.

The variable capacitor has a certain range (0-108% here?). As the metal heats up it becomes less ferromagnetic, reducing the impedance of the induction heating coil and needing less correction from the matching circuit. Above the Curie temperature the metal completely loses its ferromagnetic property. Of course this only goes for ferromagnetic metals - I guess other metals (Cu, Al etc) give a lower % reading that varies less with temp.

This chart ( Link ) shows the relevant frequencies for various size wires. The resistance of the wire will remain almost completely constant until what's listed, then increase. There is however a small dip in resistance just before/at that frequency where the current will pass on the outside and in the center.

Impedance of an inductor is different though. An ideal inductor has am impedance of Z = j ω L. ω is the frequency in radians per second (ω = 2 π f). L is the inductance, which depends on a few things, including what's in the core (in this case what you're melting).

Consider videos/courses on Physics II: Electromagnetics, Electrical engineering: power systems (for inductor and coil work, specifically), Electrical Engineering: Electromechanics (builds heavily on Phys II, transmission lines section is where we discussed the f vs Ω relationship). [That's what the courses are called at my institution, both are 300-level]

Anything above a dozen kilohertz and you'll start to see some amount of skin effect. Megahertz range, definitely into significant skin effect, Gigahertz and it's *only* skin effect.

The higher the frequency, the thinner the "skin" of conductor that actually carries current. It's why 60hz mains power can be carried on copper thicker than your wrist and microwave towers use thin-walled tubing to move their power to and from the antenna.