Right, well with the limited amount of info it's going to be difficult to come to any precise conclusions. The only info I can really provide is common faults and issues we're experiencing in the dealer network at the moment, which are.....
Thermostat housing seal failures- quite a high volume over the past year. Usually first idenitified by the coolant bottle being empty after only a few days of being topped up. Also causes a visible blue dry mark where the coolant has leaked over the top of the gearbox.
Air trapped in cooling system- vehicles are even coming from the factory like this in some cases. Can be identified by a gurgling sound coming from behind the dash on a cold start when revving the engine. Difficult to rectify in some cases, your dealer will be aware of this problem.
Water pump failure- uncommon but not unheard of.
Headgasket failure- worst case senario but increasingly common. In many cases is difficult to pin point as the only symptom can be overheating.
Radiator core failure- in some instances the radiator core begins to leak, usually in the corners.
Radiator fan failure- check to see if your fan cuts in when the car begins to overheat (around about 105 degrees it should come in if I remember rightly). This fault is most common on the Cooper S but still a problem on the One and Cooper.
That's everything I can think of off the top of my head, get back to me if you need anymore info.