Technically, the model's raw scores (logits) are divided by the temperature before the softmax function turns them into probabilities. Dividing by a number below 1 stretches the gaps between scores, so the top choice dominates. Dividing by a number above 1 shrinks the gaps, flattening the distribution.
Temperature often works alongside top-p (nucleus sampling, which keeps only the smallest set of tokens whose probabilities add up to p) and top-k (keep only the k most likely tokens). Providers set different ranges: OpenAI's API accepts 0 to 2, while Anthropic's API accepts 0 to 1. Some reasoning models fix the value or ignore it, so check the documentation for the model you use.