Exactly WHICH light is coming on? There is a "Coolant Indicator Light", it is item 3 on page 101 of my owner's manual. It looks like a radiator about half-full of coolant.

This light indicates high coolant temperature, sure - but your GAUGE will show it at the same time. IF your gauge does not indicate a problem, then the message is probably one or more of these:

1) The fan motor is not drawing current (and probably not turning) even tho the Fan Control Module(FCM) has been told to run the fan.
2) The ECM has lost contact with the FCM. If this happens and the FCM is actually working, it will go into "Emergency Mode" and run the fan at high speed, you'll hear it!)
3) The coolant level sensor is indicating low coolant (which means you are low on coolant OR the sensor is bad).
4) Perhaps other things I am unfamiliar with!