Certainly sounds like an air bubble working its way out. Is the plumbing correct after previous cooling system work? Maybe you have a leaky connection or a pinhole/crack in a cooling system hose.
I don't really know e39s, but if you can monitor the engine coolant temp sensor (not the temp gauge coolant sensor) via the OBC? It will give you a slightly different but more accurate reading and tell you when combustion temps go bad.
Maybe you have a leaky head gasket- in which case stop driving it, pull the head and replace the head gasket before it becomes a big job to do... or the cat absorbs too much coolant and dies (ie the fix requires more than just gasket (VRS kit). You could get/do a special check for pollutants in the coolant to verify the far-fetchedness of any such online diagnosis.