Estimating Text Temperature

Abstract: Autoregressive LLMs typically use temperature parameter at inference to shape the probability distribution and control the randomness of the text generated. After the text was generated, this parameter can be estimated using maximum likelihood approach. Following it, we propose a procedure to estimate the temperature of any text, including ones written by humans, with respect to a given LLM. We evaluate the temperature estimation capability of a wide selection of small-to-medium LLMs. We then use the best-performing Qwen3 14B to estimate temperatures of popular corpora.