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Replacement parts for KENMORE 11069622800 | AppliancePartsPros.com

I am assuming that changing the temperature does nothing.

Check the heating coil it may be grounded.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 10 to 12 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run on high and the thermostats cannot regulate it.

Just in case it is not a grounded element.

Check the seals (drum etc) in the unit. The air is pulled over the heating coils, through the drum and pushed out the exhaust. So any large seal leak will pull in room air and the cycling thermostat on the blower will run the unit hot.
Check that the lint filter is not coated with fabric softener residue which greatly reduces air flow.
Check/clean the blower wheel.

If all OK you may want to replace the cycling thermostat as it's contacts may not be opening (welded shut).
Be aware that this is a 4 connector thermostat so make sure to get the wires reinstalled correctly.
One set of connectors is the thermostat's contacts.
The other set is an internal heater (usually around 5000 to 10,000 ohms).
This heater is turned on for lower temperature settings adding heat to the thermostat and therefore reducing the heat output from the main heating coil.