528e trans problem

My 528e when it is cold will shift ok, when it warms up it down shifts to 3rd and then to 2nd. It will run in 2nd the rest of the time and will not shift back up to any other gear. The trans oil is ok and I have even changed it, I am at a lose as to what to look for the kic down cable is also ok.

My car did the same thing, the speed sensor was dirty. You may need a new one

My son bought a 1997 528e and we had the transmission replaced, but it won't shift up or down unless you shift it manually. I have had it off the road for almost 2 years. I am going to pick it up from the mechanic because they aren't doing anything and it will move, just shifting manually.
They say the transmission is OK, but there is some sort of electronic sensor that is bad. I am not sure and I know they don't know for sure and are guessing.
Does anyone here have any idea what could be wrong or where is a book on BMW transmissions that I could buy and I would try to fix it myself.
Thanks for any help you can give,
Ken