solenoid magnet - turns,volts,amps
First that's two different questions. 

I'll answer the second part first. More turns requires less current to get the same magnetic effect.. Correct. IN  your example you used the same current with more turns to get more field... so you need more volts to supply that current to the grater resistance. HEAT comes from power... power = volts times amps. With an ideal device that means for any given Magnetic strength, the power is the same for High V low I vs Low V HIGH I.

Induction heaters work by creating eddy currents in the thing being heated. That requires HIGH currents and frequencies.