I just went though the same thing with a 1998 Contour. I attacked the sender as I thought easier than the guage.
I replaced the sending unit and now it works fine. I believe you will find 2 sending units, one on top of the thermostat block and one underneath the radiator hose outlet on the same block. The one below goes to the guage.
What I did was to let the engine sit over night, take the top hose off and then remove the sender. You loose a little antifreeze, but I caught it in a drip pan, filtered it (using a paint strainer) and put it back.
Note, I found out the hard way that there are 2 different senders used on 98 cars, 97 should be okay but physically match it up before you take it out. Cost was under $15 at local parts store - don't know what Ford gets.
You also have to be careful when screwing it in. I think the block is a plastic type material and you could crack it of you screw it in too far (tapered thread). Someone else in the forum could elaborate.
CZ