My Kenmore Elite gas dryer was occasionally stopping in mid cycle, especially when using the hot setting. I found that the thermal cutout was being triggered. (You can check this by putting a volt meter across the terminals of the cutout switch. If it reads anything other than zero volts, the cutout has opened up, indicating overheating.) I replaced the cutout switch which did NOT fix the problem. Conclusion: the dryer really WAS overheating.
I replaced the electronic contoller board (due to a different problem) and there was no change in this problem.
I figured that the thermistor must be bad. I took out the old one and I found that it was coated with lint! The lint was sort of greasy and difficult to remove. I cleaned it off and put the thermistor back in, and the problem was fixed.
Clearly the coating of lint was insulating the thermistor enough that it was not registering the temperature of the exhaust air properly. Since the temperature never appeared to reach the threshold expected by the controller, the flame was never turned off and the dryer was overheating.
Yes, we have been using Bounce fabric softener sheets. No more! They apparently cause the sticky coating that attracts a film of lint.