My guess is a bad gauge or a bad sender. Like Tony C suggested, install a mechanical gauge and see what it says, then you'll know for sure.
The Z, once outfitted with a 3 core or better radiator, really isn't prone to overheating. I had a 3 core brass radiator and ran my car at the road course in 30 minute sessions for 2+ hours in 105 degree heat. My mechanical gauge never showed over 205 degrees. While they do have problems with vapor lock, overheating is much less of an issue.