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Parts for Whirlpool LE9300XTW1 Dryer - AppliancePartsPros.com

See the attachment for a wiring diagram.
I am not sure that it is an exact match to your unit.
Using the entire model number gave no result but using LE9300X came up with this wiring.

Since it restart right away you should be able to rule out the motor overheating.

Does it do this in both timed dry and permanent press?

Does it do this at different heat settings?

Does the timer advance?

If it does is it advancing to off every time?

Does anything else that seems strange happen?

Does it always hapen at the same spot on the timer?

Note this may be difficult to find.
Usually this problem is due to the motor overheating which does not seem to be your problem.

I was hoping that the answers would give me a clue as to what is going on unfortunately they did not.

[COLOR="Blue"]Does it do this in both timed dry and permanent press? Timed[/COLOR]
So you have tried permanent press high heat and it runs OK?
[COLOR="Blue"]
Does it do this at different heat settings? no[/COLOR]
So only on high heat?

I am sort of lost.
I does seem that it is a heat related problem.
Could be a connector is heating up, opening and then reclosing as soon as it cools a bit.
All I can suggest is that you work your way through the motor circuit disconnecting/checking/cleaning all connections.