Well, darn, sorry that happened.
There are a lot of reasons why this could be happening, but let's start with the easiest, cheapest and most likely first. I am assuming that when it shuts down it completely shuts down, and not just the heat off with the motor continuing to run.
A likely scenario is that lint and debris has built up around the motor, and that combined with the high heat settings cause the thermal protection device on the motor to shut the motor off so that it is not damaged. Then when things cool down it will run again. What you will need to do is the following.
1. Take out the two screws under the lint filter cover. These hold the top to the cabinet.
2. Use a screw driver or putty knife to release the top from the cabinet by inserting it into the gap between the top and front at the edge and prying up. The top will now flip up and flip back on hinges. Find a way to support the top so it does not flip all the way back.
3. Take off the front of the dryer by taking out the two screws that hold it on. Disconnect the wires to the door switch and mark how they go. Don't forget to reconnect them when you put things back. (If nothing happens when you try to start it up again, you may not have put them back on, been there)
4. You can now reach in on the right side under the drum and release the belt by pushing on the idler pulley to reduce its tension.
5. You can now lift the drum out. Clean out all of the debris inside.
6. You are also going to want to take off the back, and take out the four screws holding the lint chute on the machine. Then you can take off the lint chute, clean it out and clean out the blower area. Also check the vent to the outside to make certain it is not obstructed. Finally check to make certain all of the electrical connections are tight at the connection block. Check the connections at the heater element and at the thermal cutoff and high limit thermostat on the heater housing.
This is not difficult, and not as hard as it sounds. Just take your time and get it clean. Then put it back together, leaving the back off and try it out with the vent disconnected.
If this does not repair it I advise replacing the thermistor which is on the back on the blower housing. Because of the nature of your problem I do not know of a good way to test it. Here is the part
Part number: AP3919451
Your machine has a microprocessor control rather than a mechanical one, and if that is the problem then it will not be economical to repair it so lets hope the above will fix your problem. In the future I would strongly advise buying any used (or even new if you can help it) appliance with microprocessor controls.
Let us know how things turn out, have a Happy Holiday Season and thanks for serving. We are all very appreciative.