Does anyone know what to do after the thermostat has been changed and the system flushed and refilled with engine running? I'm desperate!

Hows the fan clutch? 4 or 6 cyl?

Was it overheating before you flushed it and changed the thermostat? If not they you have the thermostat in backwards.. If this was a issue you are trying to fix with the flush and new thermostat then here are a few thing to look for..Make sure to run it to full temp checking the water level with the heat up all the way. Check you belt, Flush you radiator from the motor side to the front to get the gunk ,bugs and all the nasty's out. You could also look in the radiator with the engine running and look for bubbles. If you see them chances are you have a bad head gasket that is letting hot combustion gasses in the cooling system. Good luck! George