I'm having the same problem and this is what I found. I cleaned my duck cleaned the lint area, did all the cleaning I can do. So I decided to run the unit not being plugged into the vent hose and found that the dry is staying on. Weird right! It work without the vent tube hocked up! This is what I think. The blow motor is a two function process it sucks the heat into the unit a blows it out the vent. What if the motor is no long capable of blowing against any resistance. Which reduces suction of pulling in heat. Ran a load with out the duct work hooked up, clothes are dry! I think my blow motor is no longer or is has a speed control that's not working I got to look that up. I hope this helps.
=== Update (03/15/2016) ===
This is from kenmore If the dryer takes too long to dryer or is noisy then the blower wheel could be damaged and require replacement.
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=== Update (03/15/2016) ===
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Ok this is what I found lol blower share the same motor to drum lol. No speed control. Lol but I did find something interesting the high limit thermostat, it controls the fame it it thinks it's getting to hot. So my guess is when the vent tube is off no restrictions it works just fine but when you hook the duct work up it now has a lack of flow then before. Lack of flow high limit thermostat trips shuts the gas off because lack of flow allows more heat to build up it that area. I don't think it is the other thermostat or thermal fuse because it operates just fine When the dust is off and those are on the exhaust side.
I'm having the same problem and this is what I found. I cleaned my duck cleaned the lint area, did all the cleaning I can do. So I decided to run the unit not being plugged into the vent hose and found that the dry is staying on. Weird right! It work without the vent tube hocked up! This is what I think. The blow motor is a two function process it sucks the heat into the unit a blows it out the vent. What if the motor is no long capable of blowing against any resistance. Which reduces suction of pulling in heat. Ran a load with out the duct work hooked up, clothes are dry! I think my blow motor is no longer or is has a speed control that's not working I got to look that up. I hope this helps.
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=== Update (03/15/2016) ===
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This is from kenmore If the dryer takes too long to dryer or is noisy then the blower wheel could be damaged and require replacement.
I'm having the same problem and this is what I found. I cleaned my duck cleaned the lint area, did all the cleaning I can do. So I decided to run the unit not being plugged into the vent hose and found that the dry is staying on. Weird right! It work without the vent tube hocked up! This is what I think. The blow motor is a two function process it sucks the heat into the unit a blows it out the vent. What if the motor is no long capable of blowing against any resistance. Which reduces suction of pulling in heat. Ran a load with out the duct work hooked up, clothes are dry! I think my blow motor is no longer or is has a speed control that's not working I got to look that up. I hope this helps.