Controlling temperature of a water bath with induction plate
Induction heating switches the current anyways, since a change in magnetic flux is required to induce eddy current.
$$
\varepsilon = {\Delta\Phi\over\Delta t}
$$
Plain DC would give you nothing more than an electromagnet. Therefore cycling power wouldn't really hurt anything.

Can't really advise you about interfacing with the control panel since you didn't provide any info about it and about any existing power level controls. If the on/off switch is the only available control then you might be forced to cycle power like with resistive cookers.

If galvanic isolation concerns you, then I would advise using either optical isolator or a relay together with long switching cycles.