Here are the parts
Replacement parts for KENMORE 11069812990 | AppliancePartsPros.com

Sounds like a motor problem.
What happens is the motor overheats and trips it's internal thermal protect shutting the unit off. You then have to wait for the motor to cool down so the thermal protect resets before it will start again.

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

Clean/check the interior and the blower wheel.
Also the vent system for lint build-up.
Check if there is a seal (usually looks like sponge) between the blower and the motor. Then check if it is OK sometimes it deteriorates and hot air is blown back onto the motor.

Unfortunately often this is a sign that the motor is on it's last legs.