Hi Jeremy, welcome and hope you're enjoying your Contour.
The Zetec ahs a single fan that is controlled by two relays.
The low-speed should come on at 100C and the high-speed at 103C. It is possible in a number of ways for the lo-speed circuit to be nonfunctional while the hi-speed is. This could be why your temps go up high but always come down eventually.
Open your power distribution box, and I think your owner's manual has a map of the relays. The low=speed relay is tall and green. The hi=speed is short and black.
Try this: run your engine and drive around until it heats up enough to kick the fan on, like you said. Park it, open the hood, and while the fan is still running, pluck out the tall green low-speed fan relay.
If the fan stops, that means it was your low-speed fan running, and maybe just your temp gauge is a little on the high side.
If the fan doesn't stop, that means it is the high-speed fan running, and probably your low-speed fan is not working.
In that case, first thing to try is turn on A/C. Fan should come on. If it doesn't, suspect the resistor which, as MadMerc says, is mounted on the bottom of the fan shroud and steps down the voltage during low-speed fan operation. I have had that corrode through on me. You can test it by pulling the connector and testing continuity across the two pins in the fan shroud. But I am getting ahead of myself. Test whether your low=speed fan is running or not then check out these posts:
me struggling through a similar issue, including (note MadMerc) my experiences replacing the fan resistor my summary of troubleshooting for this issue, after I got it sorted out Good luck.