Without looking at the database my guess would be that 6SE denotes the Coronet and 6SE2 the Electra, and that the serial number information would be close enough (if not the same) to date your machine. 

As for the motor I can only suggest a few of the more obvious causes of heat:
1. Is it clean or are the windings/ventilation holes packed with dirt?
2. I don't know if it has sealed or serviceable bearings, but you could check if it spins freely on its own.
3. Is there too much load on the motor? Check that all the other components it drives are turning freely and aren't dirty and/or in need of lubrication.
4. You could also run the motor without a load and check how its amperage. If you don't have a meter, you could just see how hot it runs on its own.