Hey Ldforg,
Being able to track your wrist temperature is a great feature! When checking, do you see "Needs More Data" at the top of the chart? If so, it will not track until that process completes, so make sure you have a good fit when wearing your watch. Here's a guide with tips: Wearing your Apple Watch - Apple Support
Too loose

If your Apple Watch doesn’t stay in place, or the sensors aren’t reading your heart rate, tighten the band a bit.
Just right

Your Apple Watch should be snug but comfortable.
In addition to the steps you've already taken, make sure your Apple Watch and paired iPhone are fully updated as updates install bug fixes and security updates. If updates are needed, be sure to back up first:
Update your iPhone or iPad - Apple Support
Update your Apple Watch - Apple Support
If that's all good, we recommend reaching out to Apple Support to look into this with you more: Contact - Official Apple Support
Take care!