It's part number 20 in this diagram.
http://realoem.com/bmw/showparts.do?...91&hg=17&fg=05
In my case mine was stuck open and had issues taking longer than normal to heat up during extremely cold days. I believe this thermostat controls how much engine coolant flows through the transmission oil intercooler.
If it is the same part used on your X then it is easy to change since the swap only involves coolant pipe disconnects.
I doubt that this could cause your trans to overheat from normal driving and surely would not cause a bad internal sensor reading but might be worth considering next.
Also suggest you ensure the trans refill you did is at the specified temp so the fluid level is not too low. Lots of posts about shift issues after trans fluid refills being done at too high of a temp (so the fluid is too low when it cools off). Probably something you are well aware of given your 1st post.
Gluck and curious to see your fix
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