The coolant light is on in my pontiac grand prix it's a 98 but it's full

[tiana2404]

and it runs hot. What is the problem? I have put coolant in the car to the point that I can't put anymore in. I don't know what els to do.
in the over flow jug.
the car also runs hot if I'm Idleing. It cools down when I'm moveing.

 

[melsg5]

is the radiator fan running when the engine is hot?