There is a heat exchanger thermostat in there which if defective can cause the overheating.
So in your case I would check that and the heat exchanger coolant side, don't unplug the tranny oil lines. There is a e39 link somewhere where a guy had the heat exchanger clogged and did a DIY. You can also bypass the heat exchanger and add an external cooler. There is a DIY very well done by civdiv.

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4.8is 2004 imola red
4.8is 2005 Black on Black - DINAN/2 sold
4.4 2004 X5
2003 330xi
2008 328xi - sold
4.4 2000 X5 - sold