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Replacement parts for AEM633W models | AppliancePartsPros.com

I cannot find a wiring diagram for this unit so am doing a bit of guessing.

The two sensors on your heating element are a hi-limit thermostat and a thermal fuse neither will cause your problem.
The main control thermostat is mounted on the blower assembly (Item 19 in Section 8).

Here is the guess part.
On most units in timed dry the timer motor gets power directly from one side of the line.
In auto modes it gets power when the heater is turned off by the main thermostat. It looks like your main thermostat has 3 connectors.
If yes, one will be a common. One will be normally closed, this is the contact that gives power to the heater. The last will be a normally open, this gives the power to the timer motor when the heater is switched off.

Odds are that it is this thermostat that is faulty.

Since I am guessing, please confirm that yours is a 3 contact thermostat.

There is also a possibility that you have a grounded eement re: the element has sagged or broken and is touching the case. Sometimes this can result in the heater always being on at a low heat and therefore the thermostat never opens. I doubt thuis as you said that timed dry runs normal.