The inverter supplies energy to your frying pan,via induction coil, but has itself losses.
So yes the inverter needs heat sinking, possible fans at the power levels of current you
will need.
for it to be a flying pan, the pan will need to be aluminum. the source of heat is the pan itself. the alternating magnetic field from the inverter driven coil induces currents in the pan, and the heating comes from resistive losses in the pan. IIRC commercial induction stovetops operate at 40khz. i'm not sure about how many watts of RF that's required, somewhere around 200-400 watts i would guess.
The inverter is generating heat as well due to its in efficiencies, gate losses in drivers,
esr losses in caps, I^2R losses..... Thats why heat sinks are generally needed on the drivers.
Not unusual to see water cooled induction coils as well on the higher power solutions.