this happened to my e30 a few monthes after i purchased it. my father in law was a mechanic who half owned a foriegn car repair shop, so i get a lot of repairs with no labor fee!
my e30 was overheating in the winter which i thought really sucked since it felt like it was negative 400 outside. he said it was the thermostat. he replaced it. before it started overheating the normal temp on the gauge was at the mid way mark, ie, the needle sticking straight up, since he replaced it it stays lower then that, so now my engine runs cooler then before.
from what i remember the thermostat is some kind of cork or some other material, i cant quite remember, i believe i remember him saying that when you increase the engine speed it opens the thermostat. that is why you get the engine temp increasing in the summer with the ac running and sitting in traffic. but then when you get going the temp will lower.
let me ask him again just to confirm this and make sure i am telling you the right thing. in any case good luck and have fun in your bimmer!