The analogy would be: warm is to hot as cool is to cold.
An analogy presents a comparison between two objects, aspects, so on that are quite different in nature. An analogy is intended to explain a complex subject with one that is simpler or more familiar.
An analogy may be as short as a sentence or as long as a few paragraphs.
The purpose of analogies is to explain or clarified the thing which is subject of comparison.