Overheating but oddly

My 95 TBIRD, no prior problems started running hot while on a long trip, it caused the light to come on but during an idle at a red light started cooling down into normal ranges, no leaks radiator is at normal levels. When the car runs hot the heater blows cold. Ran fine for a month then started doing it again, now it is constant. The light comes on and the temp continues to rise until I am at a complete stop then it drops to just above the midrange. If it needed a new radiator why does it not overheat? it just runs hot and causes the light to come on with out making it into the red. Any ideas welcome.

Have you checked the coolant level? If it's full of coolant, is it the proper mixture? When was the cap last replaced? If all of that is ok, I'd look into the water pump.

The fan is working right? You should be able to hear it when it kicks on inside the car. Do you usually drive really fast? I noticed that mine tends to get a little hotter when Im driving across the desert at 95mph in 95 degree heat cause I dont have the little scoop under the front bumper anymore so it starves for air.