Really reaching here, but do you have an AC unit with an inverter driven compressor? If so, perhaps a rectifier diode is blown so that it's only working as a half-wave rectifier. That would create a lot of second harmonic current and make the phase-to-phase voltage on the panel bus drop somewhat every other half-cycle. Then each 120V phase to neutral voltage would be "modulated" the same way, and maybe this is sufficient to cause the fan motors to overheat? I'm not sure why the TV would be getting hot. Maybe it has a switching supply that adapts to different line voltages and it's reacting badly to the waveform.
I realize that the impedance at the panel bus is going to be low, and so the effect I mentioned above is going to be limited but it may still be in play.
Also, I suspect that a blown rectifier could cause an inverter drive to shut down but maybe not in all cases.