2003 Chrysler Concorde Engine temp sensor jumps around

After driving about 25 miles, the temp gauge will float or sometimes jump from normal (center) to a higher temp reading.

It can go from normal to the next hotter level (60% of scale), stay for 5 to 10 seconds, then may come to center and then move back up to the same or hotter indication. There are times when it comes back to normal, but in general when it starts floatling, it only goes higher till it shows hot for about 5 to 10 seconds and will come back down to a lower reading. Some times it will come back to normal for a few miles, and then start to show hotter temp again.

The needle does not moge slowly and smoothly. It sort of jumps from one temp to the next, both up and down.

Once this starts it will do it on the road, or at Idle, and with cool temp's (45 F).

I've just got the car and don't have a lot of background on the car.

My first thought was it was a temp sensor. I looked on line and found that this engine 3.5 L and the 2.7 L engine has a history of getting sludge in the engine and reducing coolant flow.

I had the lower engine block flushed today, and the Radiator was flushed about 5000 miles ago. It didn't appear to have helped.

I should have had the thermostat replaced, but forgot to tell them to do it with trying to get the engine etc. Stuff set up.

At the dealer, it's about $250 to change the temp sensor.

Any comments or other help? Can I change the thermostat without loosing coolent and gettng air in the system?

Thanks for any help you can give.

James Yeary