The motor is not supposed to be in contact with anything flammable. Replacing a ceiling fan capacitor.

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Ceiling fan motor hot. If any of the speeds do not start and spin then a capacitor is bad. You gotta figure it should be at least 50 efficient and 30 of those watts are moving air rather than heating up the housing. Just installed a new ceiling fanthe fan works fine but after it runs for a whilewe are smelling a paint burning smell. Internal parts are typically not user serviceable so a replacement motor is your best bet. The fan is flush mount so the motor is encased and it feels rather hot. The infrared image below shows a ceiling fan motor thats hotter than the room its in.
And in the winter a ceiling fan can be reversed to circulate rising warm air. The circuit breaker wont trip and the smell will persist. It is not normally installed directly against the ceiling and the ceiling is supposed to be non flammable drywall. I know electric motors can get very hot but this is not a compressor motor its a 60 watt fan which by definition should have good airflow over it. Look for the mf number s. If you bought the 2999 special you can use it to fry eggs.
This might be why the motor is getting hot. And the cheaper the fan the hotter it will get. Fans have 1 2 3 caps or a single plastic box with 2 or 3 caps inside it. If you conect the black to the ground that is wrong and it will get hot. Because it stirs up a breeze in a room you can set the rooms thermostat 5 to 7 degrees higher dramatically cutting your air conditioning bills. A hot motor means the internal bearings and components are damaged.
It will probably do that better than move air. From the second law of thermodynamics we know where that heat is going into the cooler room. If it is smoking and flaming that would be a cause for concern. So there is no way a hot motor can start a fire. A ceiling fan makes a room more comfortable at higher temperatures during the summer. If the fan works poorly rotates slowly or not at all and emanates a burning smell the problem is likely in the motor or the bearings.
As long as you conect the wihte to white black to black and ground to the ground that is the right way to wire the fan. Because electric motors are devices that turn electrical energy into mechanical energy most of which ends up as heat. Replace the ceiling fan motor if it feels hot during this test.