What's the temperature outside and where do you live?
If you're in a place where they use salt on the roads in winter, the cooling fins on the radiator could be crumbling away. When moving, the additional airflow will cool the radiator. When standing still, the coolant temperature will rise.
If you're in a warmer climate, the radiator fan might not be turning on. People used to complain about the little bit of fan noise, so Chrysler started using a computer module to make the fan speed infinitely variable. As with all the other computers on newer vehicles, they are extremely unreliable. In addition, there was a recall to replace the bolts holding the module to the body. A good mechanical connection is necessary to dissipate heat from the module. These bolts would break, and the module would overheat very quickly and short out. These get so hot, you can burn your hand if you grab it while it's powered up. The fan isn't needed when you're moving due to the air flow. That could be why the temperature gauge drops when you're moving.
Check the coolant level too when it cools down. If it's low, the water pump can't circulate it. At higher speeds, there may be enough force to get the coolant to move. Try running the heater on the vents so you can easily feel the temperature of the air. If the air gets cool when the temperature gauge goes up, suspect lack of flow due to low coolant level. If the air gets hot when the gauge goes up, suspect the fan not turning on.
If the coolant is low and you have a rear heater, check for a green puddle behind the right rear tire. The rear hose connections have a rubber o-ring that shrinks in cold weather and leaks. There is a very effective, inexpensive repair for that. If you have a 3.3L or 3.8L V-6 engine, look near the right front wheel for a green puddle. That's a sign of a leaking water pump. It's a fairly easy repair.
Sunday, March 22nd, 2009 AT 4:48 AM