coolant temp gauge goes high when turn key

[rebuild]

89 LXi around 550k miles

Just turning the key makes the coolant temp gauge max out and stay there (whether I start the engine/drive or not) and it will only come back down when I turn the key back. On page 10-6 of the service manual I see a THERMO UNIT off to the side of the bleed bolt. Does that have to do with this problem? Engine sounds fine when it is running. No check engine light or codes. (A coolant temperature sensor would throw a code - correct?) I am thinking a faulty thermo unit does NOT throw a code.

Thanks.

AutoZone showed this for part #TU121:
http://www.autozone.com/autozone/par...ier=19140_0_0_

Not sure that AutoZone is the best place to get this part though.