I'm not a diesel guy so I might screw this up, but I believe the concern with the running temp is that the t-stat can fail and it'll run cold. You won't really get any alarms, but warning signs could be bad gas mileage. And if left to continue I think you'll start have glow plug issues, probably other things as well. I haven't really read up on it since I'm a petrol guy (for now) but here's a thread:
https://xoutpost.com/bmw-sav-forums/...-diy-pics.html