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Parts for Maytag MED5820TW0 Dryer - AppliancePartsPros.comSee the attachment for the wiring diagram.
The below assumes that it is the thermal cut-off that blew.
As mr_mjsjr said the hi-limit thermostat should also be replaced.
The cutoff is a backup safety device for the hi-limit.
If the unit is running off the hi-limit, it's contacts will eventually fail and then the cutoff blows. Unlike the operating thermostat it's contacts cannot continually turn power to the heater on/off.
Below is my standard reply when a thermal cutoff is blown.
Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 8 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 so the thermal cut-off blows.
The hi-limit should have regulated the temperature so the fuse did not blow, that is why there is a new one with the thermal cut-off (item 9 in section 03).
Note: That unless there is another problem in the unit the hi-limit should never have to open. It is just a safety device with the fuse being a backup safety device.
Just in case it is not a grounded element.
With all the below the high limit will also have to be replaced.
Check that the belt is OK.
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 your vent system.
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)