i think the sender for the dash gauge is a separate one.
i have seen where sender bulbs [the part that is in the coolant stream] turn "green" over time from [i think] lime deposits in the water used to top off, or refill the coolant system when changing out the mix.
those "green" deposits actually insulate the bulb from reading the exact temperature. shining the bulb back to the original brass sometimes restores the sender's function.
not saying it works 100% of the time, but it's well worth trying.
just something i have had experience with, and it's results.
your mileage will vary.