is the fan on its own circuit? Probably not, when you added the fan it may be causing problems in a related circuit such as another nearby light or switch. Turning on the fan causes that to overheat causing the smell which is drawn up or circulated by the fan. Worth a shot. Definitely sounds like something along the line is overheating.

Thanks for the suggestion.

This is a high ceiling in a rancher (so it's not that high) so there's no attic above.

but you could do process of elimination - what else is on when the fan is on? A light you can turn off, a computer , a TV, a monitor of some sort? In other words , shut everything down except the fan and see what happens and then if no smell turn one item at a time on.

Just for the hell of it , when the smell is noticeable go to the main power panel where all your circuits are and - careful now - gingerly touch each one to see if any of them is hot to the touch. This may give you a clue.

If worse comes to absolute worst, turn off the main power, disconnect the fan and remove it then hot wire the circuit on the fan and turn the power back on and see if the smell appears. Again, not an electrician and not sure if my suggestion is even safe. But....

It really seems to me that the fan is not the problem, you may have another problem that needs to be looked at like underamped breakers in your main panel.

Good luck

I'll give that a try.