How do you know if you have to change the thermostat for your overheating problem fan works properly but the temp gage goes all the way up and most times comes down possible stuck thermostat in jetta?

There is no sure way to know until you take the thermostat out and check it. After removing the thermostat, you can test it by submerging it slowly, with a tool in boiling water. You can then see the thermostat open up. If it does, this is not your overheating cause. If it does not, you need to purchase a new one. Install the new one and you will find out if that was the problem.