Confused

Hi Folks. I'm at my wits end. My 2010 A3 Convertible 1.6 is overheating. I've had the thermostat changed and had it in the garage but they can't find the problem. The water pump is working fine etc. After about 20 miles or so the temperature guage goes up, it fluctuates up and down and sometimes to the point where I get the red warning light on stating to switch engine off and check coolant level. The coolant level is fine and I'm not loosing any water etc.I'm wondering if there is some kind of sensor problem. When the temperature goes right up, I lose power and have no idea what to do. Any advice would be greatly appreciated.