when you say valve i'm assuming you mean the thermostat and housing?
Are you constantly topping up your coolant?
Are there any visible coolant leaks?
Is there any smoke from the exhaust?
What other tests have been done?
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.