I just had a similar problem with my 2000 Dodge Stratus. The temperature gauge would only move one notch and no further. I removed the thermostat which is located right under the radiator cap and easily accessible by removing two bolts. Upon removing it I saw that the coil was snapped and beyond salvaging. I went to the
dealer and bought a new thermostat for 16 bucks and took about twenty minutes installing it and driving around to make sure there were no leaks. As long as you put the new one back exactly in the same position you took the old one out you should be fine. Now my gauge stays just under halfway and no higher and glad to say no leaks either. I am willing to bet this is what is causing your coolant light to come on.