My phone does not register my Apple Watch as a data source for wrist temperature and it has no data.

Hi symfonie,

Thanks for posting in Apple Support Communities. First, make sure that you meet these requirements mentioned in Track your nightly wrist temperature changes with Apple Watch

"Here's what you need

• An Apple Watch Series 8 or Apple Watch Ultra.
• Sleep must be set up with Track Sleep with Apple Watch enabled.
• Sleep Focus must be enabled for at least 4 hours a night for about 5 nights."

If those requirements are met and the same continues, test with a Sleep schedule if you don't use one already. This might help since it will provide a scheduled time for sleep temperature data to be captured. The following guidance is from Set up a schedule for a Sleep Focus in Health on iPhone.

"Set up your first recurring sleep schedule

When you set up a Sleep Focus, you can set your next bed and wake up times. This schedule repeats only once. To set up a recurring sleep schedule, do the following:

1. In the Health app, tap Browse at the bottom right, then tap Sleep.
2. Scroll down to Your Schedule, then tap Full Schedule & Options.
3. Tap Set Your First Schedule, then select your options:

• Set the days for your schedule: Tap a day at the top of the screen to add or remove it from your schedule. The schedule applies only to days shown with solid-color circles.
• Adjust your bedtime and wake up schedule: Drag  to change your bedtime,  to change your wake up time, or the semicircle between the icons to shift both times simultaneously.
• Set the alarm options: Turn Alarm on or off.
  • When Alarm is turned on, you can choose a sound, its volume, a vibration, and the snooze option.

4. Tap Add."

All the best.

Thanks for letting us know, symfonie.

Since you've already completed troubleshooting, we would suggest that you contact Apple directly to investigate this further with you. You can find their contact information here: Contact Apple Support

Take care!