First thought is that the transmission oil cooler attaches to the lower right (passenger side) corner of the radiator. If the thermostat built into that attachment was damaged or it was someone not connected correctly, you could have insufficient transmission fluid cooling or be leaking transmission fluid there. The on-again off-again nature suggests it is ok when cool, but then triggers fail safe mode once it warms up. Again, perhaps pointing to inadequate cooling.

Have you checked the transmission fluid level?

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David.X5
2001 X5 4.4i Sport
SOLD! at 160k miles