Okay, I guess I'll throw in two more cents.
There are two coolant temp sensors. One is just for sending the temp to the gauge (The one that 95Mustanggt referred to) and the other is used by the computer (ECT). I'm not sure if there is some confusion about that. The one that PKRWUD and Capri306 are talking about is the one that has a multiwire connector, not the one with a single wire connector on a peg.
An ECT is about $35 so I would just replace it and see what happens.
------------------
351W 89 Mustang GT Convertible