That sounds very foul to me.
I looked up the first 110 CFM bathroom fan datasheed i could find and it has 0.2 amps nominal current. This would only increase a little bit covered up, if not decrease (depending on the fan design).
Where should it dispass all the heat. otherwise, it would bake the windings and hopefully trip the thermal protection.
I'm very sure there is another fault hidden somehwere in the house that tripped the AFCI.
