I had the exact same issue on my 2006 4.4l x5, the PO installed aftermarket sensors which were causing false readings and causing the car not to start because of "overheat issues" which it did not have, get VDO sensors and you'll be fine.
The one that goes into the thermostat and has 4 poles (4 wires) I believe is the culprit, I did change out the one on the lower hose too, thats the fan switch.
EDIT: I misspoke, apologies, not the thermostat 4 pole (that does not exist) the one that goes into the water pump was the culprit. P/N: 13621703993 and the OEM is VNE not VDO. here is the FCP link I used to get it and it solved my issues. I also replaced the fan switch on the lower hose though.
https://www.fcpeuro.com/products/bmw...ch-13621703993