Here is the wiring diagram
http://www.servicematters.com/d...0Sheet%20-%208576801.pdf

Does sound like the motor is overheating and tripping it's internal protect.
Did you replace the motor because of this shut off problem or because it was noisy or both?

Try turning the drum by hand. Should turn fairly easily. If not could be the drum is jammed for some reason. 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.

Your motor circuit is:
NEUTRAL , DOOR SWITCH , PUSH TO START SWITCH W/NO , START and MAIN motor windings 5M , BELT SWITCH , THERMAL FUSE , BU/BK timer contacts , L1

Once the motor starts running, it's centrifugal switch activates to 6M:
Parallels the PUSH TO START switch to keep the unit running once the switch is released.
Removes the START winding from the circuit. If left in circuit this would overheat the motor.

All other parts/circuits do not matter as they are for the heater or timer operation.

I would check the power to the unit perhaps one side (NEUTRAL to L1) is low causing overheating. I would check it at rest and when the motor is running, just in case something else in the unit is lowering the voltage.
Could be something weird with the belt switch or a loose connection but does sound more like overheating.
I could not find actual motor info on this unit but am assuming that the motor you replaced came with new switches. If not perhaps it is a centrifugal switch problem.

You did not say if it got hot when you ran it with no load.
If it did and stopped then I would say that your new motor has a problem.

I would check that the motor is getting 120 volts, low voltage can cause it to overheat. A bad line or pitted/dirty contacts in the timer or a switch could cause this.
Also check that the motor winding resistances are OK.
I am assuming you spun the armature and it rotated OK.

Only other thing I can think of is something is very very weird with a wiring short in the unit but the motor is pretty well self contained so it does not make sense to me what it could be.

Price for a new motor looks about the same as on this site which is usually priced reasonably so perhaps there is some thing special about this unit.
Part number: AP3094233

Glad to hear you found the cause.

A very common problem/symptom with a very uncommon cause.

Thanks for getting back to us, it is always nice to know the final outcome.
Also you may have saved someone else hours of troubleshooting time.

I am having that very same problem, how did you fix the short?

I have a GE Dryer dbvh512gf1ww and the dryer is not staying hot. The flame comes on for 10 seconds and goes out for 1 minute and on for 10 seconds in a cycle. Feels hot at first but does not stay hot. Already replaced the thermostat safty and the t- stat outlet bkup but it is still haveing trouble. What do you think.