This is getting a tad complicated.
In other words I am getting a tad stumped.

Attached is a wiring diagram for a MDET336. it looks the same as your unit but includes a timer chart and a temperature control switch chart.

During timer dry timer contacts 1A supply power to the timer motor.

During auto it looks like contacts 4 (yellow to blue) along with the cycling thermostat does this.

The circuit would be L1 , yellow on the timer , contacts 4 (yellow to red) , temperature switch L1 to C , common (blue) on the cycling thermostat , when the heater shuts off normally open (orange) (now closed) on the cycling thermostat , then to the orange at the timer which is also connected to one side of the timer motor.

We know that the Neutral side of the timer motor circuit is OK as it runs in timed dry and this side is the same in both modes.

Since it seems to be heating OK, the L1 side of the timer circuit which also provides the L1 side of the line to the heater should also be OK.
All that is left if this is true is a wiring problem or a cycling thermostat problem but both of those have been checked.
So I am lost.

You could unplug the unit and the L1 (red) and C (blue) on the temperature switch and then measure across these switch contacts. Should be 0 ohms.

If open it means that not only is the switch bad but there must also be a problem with the heater.

The only other thing I can think of is that the cycling thermostat never gets activated.
This could be a bad thermostat or if the heater is not putting out enough heat or a seal in the system is letting in room air so the temperature at the blower is low and therefore the thermostat never activates so the timer never advances.

Perhaps try low heat in an auto cycle. This setting turns the thermostat's internal heater on which adds heat to it causing it to cycle more.

It does confirm that the 1A contacts in the timer are OK but not much else.

Did you try it running at low heat seating?

Did the cycling thermostat still have the tag on the back giving it's temperatures?

You could run it while monitoring the exhaust temperature to see if the temperature is OK. It should cycle up and down about 25 degrees.

Right now all I can suggest is to try replacing the cycling thermostat.
Either it is not cycling at the correct temperature or it is never reaching the correct temperature for some reason.

One way to at least be sure it is something to do with the thermostat and not the rest of the unit would be to short the orange and purple wires on the thermostat.
I would unplug the unit and wrap a paper clip or other stiff wire between the two connectors.
Then plug it in and see if it now advances.

[COLOR="Blue"]When you say "low heat" , do you mean the delicate setting on the temperature switch?[/COLOR]
Yes.

I assume that it still did not advance the timer.

This dryer is being one stubborn son of a gun.
I am saying son of a gun but thinking SOB.

To test the fluctuation of the exhuast tempature wouldnt the cycling thermostat need to be functioning? If so, can it be doing so even though the timer isnt advancing ? What is the method used to monitor the tempature fluctuation?

Well, I just replaced the cycling thermostat and still no luck. I tried to check the heat fluctuation with my hand but it was hard to tell for sure. The thermometer i have wouldnt go high enough either. I recently rewired the dryer recepticle and the problem seems to have started around that time as well. Is there a chance the wiring is wrong although everything else is functioning correctly?