One problem related to radiator has been reported for the 2012 Mini Cooper. The most recently reported issues are listed below.
Temperature sensor in radiator hose leaking. Needs upper radiator hose, and thermostat with harness to correct. Discovered during a routine oil brakes etc inspection by the dealership. I was told there was a change in the harness and the new one has a "computer" and would cost $1450 to fix. This is an upper hose and I looked online and found the replacement harness has tow separate connectors, one for coolant temp sensor and the other for the coolant thermostat. I hd checked my fluids two days before on a cold engine and they were fine and water overflow was at the proper level. I checked my coolant overflow tank the day after visiting the dealership on a cold engine and the overflow tank was low. . . I added water. . . It has not gone down for several days. I have heard there is corrosion that happens and the thermostat may not employ and you can have an overheated engine.