What is making my car overheat?

[shoelacesrkool]

It seems that the message telling the fan and the gauge how hot the engine is getting is not going through properly. There is antifreeze going through the engine, but the temp gauge stays around the cold mark until the antifreeze boils over, then the needle shoots up way past the hot mark. The fan also doesnt turn on until a bit before that. What part do I need to replace? my guess is some sort of sensor, but I don't know. I can do parts and wiring and whatever, but no ECU stuff. It's a 1987 Mustang LX notch with an auto 2.3L.