I replaced my temperature sending unit a few weeks ago. Yes, it's different than the coolant temperature sensor that goes to the computer. So it won't affect how your fans come on, etc. However, I do have a duratec, so your zetec may be a bit different. But I think the general principle is the same. It's a little hex-shaped thing.
At any rate, it was a super easy fix on my SVT. About 10 minutes.
One thing about your post concerns me, however. My gauge pegged way past the "L," and it stayed there until I fixed it. Your gauge staying at the cooler end may be indicating something other than just a bad unit (loose or cut wire, etc.).
