"s.morra" asked a question about the concept of "thermal inductance," in an
effort to explain a heating/cooling phenomenon. Since we know there is
thermal resistance (the reciprocal of thermal conductivity,) and thermal
capacitance (product of mass and specific heat,) it seems as though, by
analogy, one should look for thermal inductance as well.

The first thing to note, here, is that heat flow is described by the
diffusion equation, while electrical phenomena obey the potential equation.
These are two separate differential equations, so it does not surprise me
nor trouble me that inductance is absent from all heat flow phenomena.

I doubt that the fast heating of a quenched rod really happens. If it were
a tube, I can attest that it does happen, because steam travels up the
inside of the tube. Possibly, something like that can happen to a lesser
degree on a solid bar, but I suspect that it is mostly psychological. It
would not be hard to do a test. I have a torch, and I have a Fluke meter
that can be hooked to a thermocouple. In fact, this would make an excellent
science fair project, but I'm a little old for that. However, if there is
enough interest, I would be willing to carry it out and report the results.