2001 Taurus Low coolant light

When the car is cold, the low coolant light comes on and does not go off. After the car has been driven a while and the car is warm, if the car is shut off and then restarted while it is still hot (warm) the light does not always come back on (some times it does, sometimes it doesn't). The reservoir is full and I see no signs of leakage. I can't find a "radiator cap" with all the shrouds under the hood in order to verify that the radiator is actually full. Is there one? Could it be a sensor or a float and how do I isolate it down to a single component?