I don't think watermarking breaks this relationship. Watermarked text is still being sampled from the model's output distribution, and adjusting the temperature

I don't think watermarking breaks this relationship. Watermarked text is still being sampled from the model's output distribution, and adjusting the temperature still has the same affect on that output distribution. I think a good intuition here is that watermarking is sort of like picking a specific PRNG seed. It's not changing or interfering with the temperature - we're still sampling from the model's probability distribution. But we're making it so the analog of the PRNG seed is coupled to the previous context.