How to repair the coolant temperature harness that has been cut?

It depends on where the wire is cut and whether the connector is damaged. If there's enough of each end of the cut wire that you can strip the ends, check out this video on wiring repair:

https://youtu.be/4TjSYfLTHfg

The main thing is to seal the soldered splice with moisture-proof heat-shrink tubing. You can find it at any auto parts store and most hardware stores. Never use electrical tape as it will unravel into a gooey mess on a hot day.

If the connector is damaged, all auto parts stores have huge books showing just about every connector for any car model and engine size. I prefer to find the same engine in a salvage yard and snip the connector from it.