Sounds like a motor problem to me.

The thermostats should reset much quicker.
What is happening is that the motor is overheating and tripping it's internal thermal protect. You then have to wait for the motor to cool down and the thermal protect to reset before you can restart.

Try turning the drum by hand. Should turn fairly easily. If not could be the drum is jammed for some reason overloading the motor.. You may want to try this on a couple other dryers to get a feel for it.
If it is difficult to turn run your fingers around the back and front of the tub to machine seal. To see if something has jammed between the tub and frame (bra wires are famous for this). Be careful in case the object is something sharp.
If nothing is jammed in there you will have to open it up and find the cause.

If it rotates OK then odds are that the motor is toast.

You did not mention a problem with the heat so I am assuming that the centrifugal switches on the motor are being actuated.

Check that the blower is sealed correctly, have had one where heat was being blown back on the motor and causing it to overheat.