If, as you described, the gauge falls to the bottom of the range within seconds, that's way too brief a time for the thermostat to be at fault. But this behavior is typical of the often bad temperature compensation board.

Do a search on this forum and you will find literally hundreds, if not a couple of thousand, posts that involve this nuisance.

My suggestion -- remove this board and replace it with a jumper wire (you'll find instructions in those aforementioned posts), and you'll now have an accurate temperature gauge for the first time! [noting that the original design of the TCB is to lie to the driver.]