If it is an older dryer then check on the back for some round looking things with wires going in one side and coming out the other. These are heat sensors of some kind and they, among other switches and such, tell the machine when to run and when to stop.

If one of them fails you will get this type of action since it is telling the machine to stop, then to start, then to stop.....

But the good thing is that it is a Kenmore. This means you can go online and buy for just a few bucks a repair guide for your machine.

These are not complicated devices, at least the older ones are not. And if you have a voltmeter and a phillips head screwdriver you can almost fix anything on them.