Why the current flowing through an induction heater increases when something is heated up?
Changing the current in an inductor causes a changing magnetic field around the inductor.  The changing magnetic field induces a voltage opposing the changing current in the inductor, thus limiting the peak AC current.  Place certain materials inside the inductor, and the changing magnetic field will induce eddy currents in that material which will reduce (rob from) the magnetic flux, which will decrease the back EMF on the inductor coil, thus allowing the current in the inductor to change more easily up to a higher AC maximum.  

The resistive losses of the eddy currents will both heat something up, and allow the eddy currents to continue “robbing” even more of the energy from the magnetic field, further reducing back EMF on the coil, which then can allow even more current to flow.