Temp gauge issue?

I have a interesting issue with my Mercury Sable v6 3.0 liter. Car temperature is constantly fluctuating from about 3/5 of the way up to cold. This will happen at least once every time I drive one mile at 65 miles per hour. I have changed the t-stat. This is not the issue. I also know that there is no oil mixed with water or oil mixed with the antifreeze either. There is no white smoke coming from the tailpipe. Also the heat will work all the time. The car will run fine except when in park the rpm will fluctuate from 1000 to about 1200 about once every 10 seconds. Could these 2 issues be related? I have not tried a coolant temp sensor yet but I'm thinking about it. I'm just trying to avoid a very costly repair bill.