During cool times the thermostat is necessary for maintaining engine temp. This means if its stuck open the engine won't heat up. Let me tell you that a stuck open thermostat won't make a hoot of difference to engine temperature in Florida most of the year (with the posible exception of diesels and M110 motors). If you run 70 for 5 miles on a 80+ deg day and are reading in the 40's then you have a gauge problem.
The sensor is on the left side of the cylinder head and has a single wire. I never remember the ohmic values but disconnecting it should cause the gauge to go hot or cold with the key on. Grounding the wire should make it go full range the other way. The old 126 dash printed circuits used to get bad connections where the fuel and temp gauges screw to the board. The sensor is cheap enough it might be worth it to just replace it from a diagnostic sense.
If you would like an ohm value let me know and I'll measure one; if I don't have it written down somewhere in the shop.
Owner 24 bay BSC
Bosch Master, ASE master L1
26 years MB technician