Are there any wearables, wrist-based or rings, that allow you to export minute-by-minute skin temperature data?

Quantified Self Apps & Tools
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Want to track distal-proximal temperature gradient during sleep.

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this one recently launched by polar might:

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It seems that you will need to measure at multiple locations. I think iButton will suit your needs.
I’ve used it (have 3 of them), you can read my results in this my my blog post Circadian rhythm of body temperature with iButton.