It's not temperature, but sampling. Output of LLM is probabilistic distribution over tokens. To get concrete tokens, you sample from that distribution. Unfortunately, OpenAI API does not expose the distribution. You only get the sampled tokens.
As an example, on the link JSON schema is defined such that recipe ingredient unit is one of grams/ml/cups/pieces/teaspoons. LLM may output the distribution grams(30%), cups(30%), pounds(40%). Sampling the best token "pounds" would generate an invalid document. Instead, you can use the schema to filter tokens and sample from the filtered distribution, which is grams(50%), cups(50%).
Not traditional temperature, maybe the parent worded it somewhat obtusely. Anyway, to disambiguate...
I think it works something like this: You let something akin to a json parser run with the output sampler. First token must be either '{' or '['; then if you see [ has the highest probability, you select that. Ignore all other tokens, even those with high probability.
Second token must be ... and so on and so on.
Guarantee for non-broken (or at least parseable) json
