The thermostat is independant of your transmission. It is on the opposite side of the engine.
If you were having maintenance performed on your water pump or cooling system, then the thermostat would come into the mix. But, not for transmission work.
Your car is a the age/mileage where a thermostat could fail. Sometimes they last a real long time and sometimes they don't.
2013 535i - ED, Oct 2012 | Cashmere Silver | Oyster/Black Nappa Anthracite | ZCW | Sirius | Air Blue 80
2008 X3 | Monaco | Sand/Black Light Poplar | ZAP | ZPP | ZCW | Xenon | Rear Fog
1988 Grand Wagoneer | Burgundy | Ghost Flames | 360 ci | Holley carb
BMW CCA #422951