The given model number comes up as a washer, please check it.

Sorry but I cannot find any info on the new given model number tried AppliancePartsPros and the Frigidaire site.

I really need a wiring diagram, even with it I am not sure that I can be of much help.

Your problem is weird in that it sounds like the motor is overheating and tripping it's internal thermal protect but you do not have to wait to restart the unit so I do not think that is your problem.

You did not say that the drum was hard to turn so I am assuming it is OK.
Having to spin the drum is often a motor problem but I do not know what would stop it and then let it restart right away by just re-spinning the drum.

It could be a bad centrifugal switch on the motor problem here is that usually you will hear the motor buzz/hum when it tries to start and you did not mention this.
My thinking is that the centrifugal switch is no good so the start winding is not in circuit so you have to spin the drum to get it to run. Then the centrifugal switch opens after 15 minutes and stops the unit.
To be honest this is a long shot and I do not have much confidence that it is correct.

Could also be a bad spot on the timer cam if the motor stop is always at the same spot in it's rotation.

Check inside the control console, often the wiring diagram is in there.