Bathfans, turn tables, rotating window displays, and so on so forth requiring low torque motors utilize an inexpensive motor design usually 1/10 hp or less which incorporates a shaded pole priciple in the motor magnetic laminates to produce a rotating field or magnetic pull on the motor armature. Locked rotor current on these motors is only slightly higher than normal running current due to thier inherent poor efficiency to begin with.
To me lint collecting in the fan would likely be what causes a fire. As stated also the wear and friction of the motor shaft with sleeve bearings getting hot may be more likely the cause than a winding failure