Hi @gurlygurl4658 ,
Does it get hot and stop on all 3 of the speed settings?
I don’t know how your particular fan is wired but if it only does it on one speed setting it may be that there is a faulty capacitor connected to the switch for that one speed which may allow extra current to flow through one of the fan motor windings making it get hot.
In a lot of electrical motors there is an integrated thermal switch in the motor itself, which operates to stop the current supply to the motor, if it gets too hot, preventing it from burning out. Once the motor cools down the switch releases and the motor can be started again, only to go through the same cycle if the problem is still there.
If it occurs on all 3 speeds, then perhaps the main run winding has gone faulty and is allowing extra current to flow making the motor get hot.
Are the air intake slots around the fan motor housing clean and free from dust etc? If not, this may impede the flow of draft air through the motor, preventing the heat from leaving the motor, which helps it to keep cool. Just a thought.
Here’s a link to the ifixit How to Replace the Fan Blade Assembly on the Utilitech SFC-1 500B 20 " High Velocity Floor Fan guide, which may be of some help to gain access to the fan motor.