It looks like P112B is a Coolant Temperature Sensor code. That would explain your wonky temperature readings. Check the electrical connections to the sensor, if that doesn't do it you may have to replace the sensor.
Also, if your coolant was low you should bleed the system when you top off. There are directions in this post.
e53 2003 X5 3.0i - 9/03 Build Date
e30 1985 318i - Retired
BMW CCA Member # 304467