I think it's right under the coolant fill cap. I have a 2003 mini, and I can see the radiator hose going in there, but it's hard to look in. I copied the instructions from autozone.com and will paste them below. The instructions don't mention it, but I think you will need to remove the air filter housing to access the thermostat housing bolts. Also, there is a bleeder port on the upper radiator hose that I would crack open after the job is done to let any air out. The instructions don't mention that either, but it's always good to bleed the system. Let me know if you have more questions.
If the radiator is filled to the top with coolant and the engine is run without the radiator cap in place, the coolant will expand and spill over as the engine warms up.
- Drain some coolant into a clean container until the coolant level is below the thermostat housing.
- Remove the upper radiator hose connection from the thermostat housing.
- Loosen the housing bolts and remove the housing.
- Remove the gasket and scrape it carefully from the surface of the housing and the mounting surface on the engine. If the gasket remains on either of the surfaces, there will probably bea coolant leak after reassembly. Some engines use a rubber O-ring to seal a thermostat housing.
- Compare the size of the thermostat to the old one. They are of different sizes, types, and temperature ratings.
- The temperature rating is stamped on the sensing bulb on the bottom of the thermostat. The temperature bulb faces the block.
- When replacing a thermostat, be sure that the thermostat fits into the groove in the block or outlet housing. If the thermostat is installed upside down, the engine will overheat.
- Install the gasket.
- Reinstall the thermostat housing. Refill the system and run the engine or pressure test to check for leaks.
- When the engine has reached operating temperature make sure the thermostat opens.
- You should be able to see coolant circulating within the radiator.
- Another way of checking thermostat operation is to feel the top of the radiator hose or use a thermometer or multimeter with a temperature probe to confirm that the coolant is warming up.
- If the engine is overheating, but the top hose is still cool to the touch, the thermostat is stuck closed and must be replaced.
When a paper gasket is used and the recess is in the thermostat housing, it is a good practice to position the thermostat into the recess and glue the gasket to hold it in place. If it falls out of its groove during installation, the outlet housing can be cracked or a coolant leak will result. Before tightening the water outlet housing, try to rock it back and forth to be sure it is flush. Housings are often cracked during this step.