Without a model number for your Kenmore dryer, it is hard to predict the exact cause of your failure. I would also need more details. Here are some general tips that may help:
Some overheating problems are caused by restricted venting. If the dryer is
, I recommend running a test cycle with the flexible vent disconnected so that the dryer exhausts directly into the laundry room. Check to see if it cycles properly at normal temperatures when drying a medium load of wet laundry. Some dryers will heat up to 150 degrees and then turn off. They will cycle back on at about 140 degrees. Some will heat up to about 180 degrees and cycle back on 10 degrees below that. If the dryer heats and cycles properly while venting directly into the laundry room, then it is almost certain that a blocked exhaust vent is causing your overheating problem. NOTE: This type of test is not normally performed on a
dryer. Gas dryers must always be vented properly to the outside of the home. (A much shorter test could be performed on the gas dryer to check the cycling temperatures.)
If the temperature in the dryer goes up to more than 200 degrees and then cycles off until the dryer cools back down, you could have a failed operating thermostat. This would cause the heating element to be cycling off of the high limit safety thermostat.
A heating element that is shorted to ground would heat constantly and not cycle off. This could be causing your overheating problem.
If these general tips do not help you resolve this problem, I recommend resubmitting your question with addition details (cycling temperatures) and the full model number of your Kenmore dryer.