Temp gauge rises with headlights on

I'm thinking it's engine to chassy ground.

So? CHECK IT LOL Hook a meter to the engine block and to the battery NEG post on low DC volts. Turn the key on to activate the temp gauge. Now turn on the headlights. Any reading? Should be zero

I doubt this is the area of the problem. An engine ground that bad would probably give you other problems.

More likely this is a problem with gauge / panel grounding. Some of these gauges are what is called a 'bridge' circuit. The gauge itself (or ground terminal on the gauge) must be grounded.

Another thing you can try is with the key on, and headlights on, run the instrument lamp dimmer up and down and see if that changes the gauge.