low coolant

the low coolant light comes on on my 01 gt 3.8 but the coolant is full in the radiator and the over flow
some times the light will go out for a while but it always comes back on

ANY SUGESTIONS WOULD BE GREAT thanx

There's a sensor on the radiator which trips the light when it's low. If coolant is fulled to the neck of the rad, and the light is on, it could be a faulty sensor. I've never replaced the sensor, I don't know if it's something that could be cleaned or not.