I don't think you'd achieve much by changing the resonant frequency. At that frequency inductance and capacitance cancel out leaving you with a resistive load (the item being heated) as it appears like a resistor across the secondary of a transformer where the inductor is the primary.

 

yes, having ead some more, it appears that the heating rate is mainly affected by:

• Field strength of the magnetic flux field
• Coupling of the induction coil to the workpiece
• The electrical and magnetic properties of the material being heated

(Page 16 - http://www.elegron.pl/files/TheoryHeating.pdf)
As for the final temperature which can be reached, I haven't got to what influences that one yet, but I suspect, looking at commercial devices it's about the power which can be generated in the tank, and also the efficiency with which this can be transferred to the workpiece, so close coupling of work coil and workpiece, perhaps using a crucible which might conduct more heat to the workpiece and act as an insulating container.

 

The power radiated by hot material is proportional to the fourth power of absolute temperature (Stefan's Law) - approximately, as it isn't a perfect "black body". The circuit has supply more power than is lost through radiation, convection and conduction.

 

As for the final temperature which can be reached, I haven't got to what influences that one yet, but I suspect, looking at commercial devices it's about the power which can be generated in the tank, and also the efficiency with which this can be transferred to the workpiece, so close coupling of work coil and workpiece, perhaps using a crucible which might conduct more heat to the workpiece and act as an insulating container.

I saw a cool thing on this induction heating topic last week. They were in a nonferrous casting foundry, and instead of gas to melt the metal they use induction coils around the crucible. As the aluminum they were melting got molten they had to dial back the frequency on the control panel. If they didn't the aluminum was starting to rise out of the crucible just like an aluminum fountain, they only let it happen for a very short while to show the people filming. But they said it would if left go at that frequency it would empty the crucible onto the floor.