Cannot find any info using given model number.
Kenmore numbers are usually XXX.XXXXXXX all of them being numbers.

Not sure what you mean by"short cycling". Could you please explain exactly what is happening.
If it is that the heater is turning off/on quickly and not developing much heat, I would try the following.

Undo the dryer from the exhaust
Run a load
If the load dries correctly then you have a vent problem.
Clean/check the vent system. Make sure the outside louvers open fully.

If you do not want lint in the house.
Take a pair of pantyhose, put one leg into the other and attach this to the dryer exhaust.
Leave enough room behind the dryer so it can blow out like a windsock.
Run a load.

Both the above will allow you to check the air flow and temp.
Also the above is NOT recommended for a gas dryer due to possible carbon monoxide problems.

Here is a manual which I think may be close to your unit. I know your unit is a Frigidaire but there is no way to cross reference the model numbers so I found a manual where the control panel looks close to yours. I hope!!
http://frigidaireservicetips.co...rGoodandBetterModels.pdf

Would unplugging the moisture sensor make a difference?
It can't hurt. I would try cleaning it with isopropyl alcohol first.

I also would pull the thermistor and check it for resistance.
The manual says it is a negative coefficient thermistor so as temperature increases resistance decreases. Check that it is within spec at room temperature. Then hold it on an ice cube the resistance should increase.
Then hold it in your hand and it should decrease.
Check that the wires from the control to the thermistor are good.

You are welcome

Glad it worked out

Thanks for replying back because another person with the same problem will see how you fixed yours and that it worked.