Don't worry!!
Sounds pretty typical for short distance, stop and go cold weather driving....these motors run pretty cool. However, that said, if you haven't replaced your water pump/thermostat/thermostat housing by now, this is a good time to do it!
Don't forget to use BMW anti-freeze and you can order all the parts from BMW. If you aren't handy with a wrench, this isn't a difficult job for most amateur wrenches or most shops.. shouldn't cost more than a couple hours work.
"Uncle" Phil C
2011 Kia Optima EX-P.
Former owner of a 95 525i 5spd. "The GQ" aka A Shark in sheeps clothing
03 R1150RT 6spd. "DaRTth"
00 R1100R 5spd. "LeRoy"