My dryer shuts off in the middle of the drying cycle. It won't start again until it cools down. I have taken the back off and cleaned all lint away from vents and the motor. I have cleaned all vents and hoses all the way to the outside of the house. The unit is about 3 years old. Could it be a moisture sensor.

That sounds awfully a lot like a bad motor. Can you tell if it is "straining" to run? Possibly sounds louder than it used to. Also make sure the drum can turn easily an there is nothing restricting it such as worn drum slides or a tight rear bearing.