Hi and Welcome,
I to have a TD5 overheating problem, in my case new radiator and pump, I don't know about the thermostat but my fan hub is faulty.
I don't know the 'official' way to test it but if the motor is hot the fan should be hard to turn.
There is a gel in the hub, when cold it is stiff to turn when it warms up it seems to get runny, easy to turn but when it gets up to a certain temp it goes thick and ensures the fan works to draw air through the radiator.
If your motor is over hot and you can turn the fan easily it is faulty.
With my motor running and the shroud off I can (very gingerly, it's probably not recommended)

stop the fan, even spin it backwards, it's stuffed!
Good luck.
Mike
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