My car has a 2.8CRD Diesel and its target operating temperature is 80C or 176F so it seems to me that the temperature is there and close to right, unless it is supposed to be so much hotter. If the thermostat was stuck even partially open the hose from thermostat to radiator would warm up as the engine warms up - it should stay cold until the enging is warm enough to open the thermostat. I have a stuck open thermostat on my Grand Voyager (Town & Country) and to prove it to myself I did just as described above.
I dont know if it is your problem, for example it could be a water pump problem too I suppose, but it does seem a good bet. Open the hood and monitor the radiator hose temperature first thing on a cold morning and see what you think
2007 Chrysler Grand Voyager 2.8CRD
1998 Dodge Grand Caravan
1998 Chrysler 300M
1994 Chrysler Intrepid