temp warning question

[feelstranger]

hey folks, hope I can get some input about an issue.
After the car sat for 2 weeks or so, I drove it yesterday and was greeted by a blinking-red-three-beep temp warning alert  - however, I had only been driving in town for about 10 minutes tops and the temp gauge and oil temp gauge were both reading like the car was not yet warm (vermont ~ 20 F) .  Same thing happened today after a short drive - water and oil temp gauges just above cold and then BEEP BEEP BEEP.
Can the MFTS signal an overheat danger signal even if the temp gauge shows low temp and the actual temp is likely low?
is it possible for a thermostat to fail closed or something and cause a weird problem?
TEA
Nat