Originally Posted by fmugur

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.