Hay! So you did get the E28 after all! Congrats! How is it?? Wheres the pics!
Regarding the Temp Sensor , Im not sure if its the same as that of the E30 .. Is it? Blue and Brown temp sensor? One goes to the Dash and the other goes to the ECU .. You should test Both with an Ohmmeter , Also the one going to the Dash , Try testing it buy removing it and putting it in hot water , just the gold part , not the whole sensor ,Also the water does not need to be boiling hot water but Warm to hot water and see if your gauge moves . If it twitches at least you know that there is some sort of connection between the Sensor and the dash.
Those sensors are not expensive though , You can get them from Diesel Electric as well . BMW wasn't expensive either . So I advise changing them anyway . They can get old and faulty giving off wrong readings to the Computer or the Dash.
If the Temp Gauge on the dash is faulty , Take it apart and have a look at the soldering joints . I read that over time these can get loose or corroded and cause this issue , Also If the wire from the Gauge to the temp sensor is damaged , That might cause it .