Located in the air intake filter box is a auxiliary thermostat. Made out of plastic, so over time (decades) it becomes brittle and it's two hose fittings tend to crack at the base and brake off. Either scenario is highly undesirable, as it sure will cause leak in the cooling system with following overheating, etc.
I do all my car repair at TechShop, Menlo Park (http://www.techshop.ws/), conveniently located just a few blocks from my house. They have a nice car port with plenty of heavy duty car tools.
Step 1: Getting the Parts
When initially confronted with the problem of getting the right part, you get mad at the fact, that this little part is sold by BMW dealerships for over a hundred bucks. You'll find plenty of forum posts on the web, where people just recommend bypassing the thermostat all together. Instead of doing that, I'd recommend getting it from an OEM supplier, same exact part made by Wahler for BMW production line sold at around $50 at PelicanParts.com.
Step 2: Get the Thermostat Out of Air Intake Box.
Thermostat has two hoses attached to it, and it's easier to detach it from the air intake box, rather than getting to two clamps to detach the hoses. Space is tight around it, so you'll need to use a flex shaft with a 10mm socket to take a single screw out. Once out, first mark one of the hoses with tape to remember it's position and detach both hoses from the thermostat. (See cracked base of the hose fitting on second photo).
Step 3: Attach Hoses Back to New Thermostat.
After visually inspecting integrity of the two hoses, and making sure that there are no cracks, attach both hoses back on the new thermostat fitting one at a time using original clamps. Do not over tighten, fittings are plastic and will brake easily.
Step 4: Bleed Air and Verify Installation
Bleed air out of the cooling system, check everything to make sure that you properly installed the part, that you don't have any extra screws left and no tools in the engine compartment. Start the engine and after few minutes verify that there is no leaks in the area of newly installed thermostat. And you're done!