This is a single phase ac motor that uses either a start or a start-run capacitor. It is that black lump on the top of the motor housing. The purpose of the capacitor (cap) is to change the timing of the AC phase between the windings and the armature. Caps are designed to pass AC and block DC current. As capacitors get old (over years) they start to pass DC and eventually will fully short. So instead of the winding seeing AC, they are seeing AC riding on a DC current, and the windings are not designed to pass DC and will heat up (act like the grid in a toaster).
Before you condemn the motor, find a friend that has electrical knowledge and have him test the capacitor. Capacitors cost typically less than $25. You will be hard pressed to find a motor of the quality you have now for less than $125. Don’t buy a replacement cap on Ebay or Amazon. Use an electronic supply house (Digikey, Newark Electronics) as there are many counterfeits out there. Stick to a name you have heard of (Sony, Panasonic, etc,). The voltage rating must exceed 220 and the Farads should be the same as you have now and have a temp rating of 110C.