You most likely have a large air bubble in the cooling system. Your engine really is not running fine, because it is telling you that it is hot.
Any mechanic that tells you to just ignore the temp gauge is not only a bad mechanic, but he is probably also not familiar with how to bleed a BMW cooling system. It needs to be bled propperly. The links above will explain the process. I would not let that mechanic work on your BMW any more.
It is possible that there is a thermostat problem, but an air bubble is a more likely scenario. What brand of thermostat is it?