I just picked up a 2001 Jetta 1.8T for next to nothing today and it is in excellent condition. The only thing that I noticed that is wrong is that the temperature is somewhat erratic.

You will be driving down the road and it will be at 190 degrees and then it will climb up to 240 or so for a bit and then will then shoot back down to 190 degrees. What I'm thinking is that the thermostat needs to be replaced. Am I correct?
If so, how easy is this to change out myself? Do I need to change the coolant at the same time? I'm guessing that I'm going to lose some of it when I unscrew the thermostat.
Thanks.