If your drier is not heating, first check the exhaust system. If the exhaust vent hose is kinked or if the vent or hose is blocked up with lint that will restrict the airflow and the nigh limit switch will immediately open, causing the heating element to shut down. Try disconnecting the hose from the drier and see if it will heat up. If so, you may have to clean the hose, through the wall vent tube, or the internal parts of the heating section on the drier.
If it does not heat with the hose disconnected, pull the power cable to insure there is no power to the drier, then remove the back cover. Locate the heating element and disconnect the wires from the heating element. Be sure to note the location of the wires so you can get them back on the same terminals.
Now test the heating element with an ohm meter. With one probe on each contact on the heating element you should get a low ohm reading, typically 5 to 10 ohms. If so, the element is good. If the ohm meter shows zero resistance the element is burned out.
If the element is okay, replace the wires and locate the thermostat on the air duct. It looks like a round plastic disc about an inch in diameter with two wire terminals. Remove the wires and check the switch with the ohm meter. If it is good it should show continuity when the drier is cold. If there is no continuity the thermostat is open and will need replacing.
Next check the high limit switch. It will look like a thermostate too, but it is mounted either toward the top of the air duct or very close to the heating element. It should show continuity when cold.
Sears Kenmore appliances are primarily built by Whirlpool. I have had success in finding parts for whirlpool or kenmores that were twenty years old and more.
Normally sears will only supply the parts for about 5 or 6 years, then they tell you its no longer available, which of course it isnt through their supply chain. Lets face it, sears is in business to sell appliances, not service them.
Copy down the full model number and serial number before trying to find the parts.
I find the best source is to locate an appliance parts supply house as they not only have access to the OEM (Original Equipmnet Manufacturer) parts, but they also have access to generics. (Often the generic part is coming directly from the same source where the equipmant manufacturer is buying thier components.
As electric drier is really a very basic circuit. Usually it only has the heating element, thermostates and high limit switch in series.