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Induction heating works by using induction to transfer energy from the power source to the object wished to be heated. The system is designed and optimised for that purpose, it is not just a coiled-up mains cable, and while the object gets hot, the primary induction coil stays relatively cool...

The inductance is irrelevant. It is only the resistive component that dissipates power.

It is a long, long time ago that I learned electrical theory, so the laws of physics might have changed since then, but I was taught that ideal inductors were reactive components and thus did not dissipate energy. Real life inductors dissipate energy mainly because they also have a resistive...

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