This article is from the Chrysler-Plymouth-Dodge FAQ, by Dr. David Zatz with numerous contributions by others.
Robert Rowe: With the ignition on, ground the wire coming of the
sending unit momentarily while the enging is warm. If the gauge moves to
the correct temp, the sender is at fault. Do not ground for a long
period of time as this can damage the gauge.
Peter Galambos: Temperature gauge would suddenly jump to 3/4 or almost
full scale for a few seconds and then drop back to center. I hooked a
voltmeter to the temperature sender input to the body computer and
actually saw nice linear voltage swings. It appears
that the gauge is designed to go super non-linear above a certain
temperature. I disconnected the radiator fan long enough to verify that
it was thermostat cycling causing the temperature swing and replaced the
thermostat and antifreeze.