Wrist temperature not working

I'd contact Apple directly for guidance. Since you own Apple Watch Ultra, even if you didn't add an AppleCare+ plan, you're entitled to 3 months of free technical support by calling Apple (if in the US) at: 800-MY-APPLE

Did you follow the directions in the related article link you came here from, which shows you how to use the sleep app to check your temperature while you sleep, which takes time for the data to be collected? This would require you sleep with the watch on and sleep set up to track.