The temperature parameter in Large Language Models (LLMs) can be understood through the lens of statistical physics, specifically the Boltzmann distribution. In physics, this distribution describes how likely a system is to occupy different energy states. The temperature variable dictates how much energy differences matter, with low temperatures amplifying differences and high temperatures flattening them, leading to near-uniform probabilities.

This same mathematical principle applies to LLMs when they predict the next word. The model's raw output scores, called logits, are analogous to energy states. The Softmax function, which converts these logits into probabilities, is mathematically identical to the Boltzmann distribution when the temperature parameter is included. A temperature of T=1 represents the model's learned probabilities. Lower temperatures (approaching T=0) make the model more deterministic, always choosing the highest-scoring word, which is useful for logical