Is it possible to have a problem that keeps causing a thermostat to stuck open? I replaced it once and it was stuck open. Everything was fine and car was nice and warm. Now this longer I suspect is stuck open because the car is cold again.

 

It's possible, as thermostats are designed to fail in the Open position, as it's less of a problem for the engine to operate over cooled, than over heated!
If your in dash temp gauge is reading cold & or you have a lit CEL with trouble code clues that indicate the engine isn't reaching operating temp, a stuck open thermostat would have earned its place high up on your suspect list. An OEM part, or one designed like it, of the specified temp operating range, is recommended.

Let us know what you find.

 

Yes, it's possible. It's better to have it stuck open than stuck shut. Buy a good aftermarket one and test it first by boiling it in a pan of water with a thermometer to see when it opens and closes.