Beyond the natural philosophy, fire carries a set of working attributions in the Western esoteric tradition, and those attributions belong to particular systems rather than to the element as such.
In astrology fire is a triplicity, a group of three signs standing at a hundred and twenty degrees from one another: Aries, Leo and Sagittarius. The grouping is old, it is in Ptolemy, and it is the mechanism by which an element attaches to a chart at all. Nothing about the individual signs follows from the element on its own.
In the tarot, fire is conventionally the suit of Wands, and in the Golden Dawn system it is placed in the south, given the wand as its working implement and the archangel Michael as its regent. Those attributions are documented, they are internally consistent, and they date from a specific late nineteenth century synthesis rather than from antiquity. A different school assigns the wand to air and the dagger to fire, and the disagreement is old enough that neither side can be called an error.
The Hebrew letter shin, the Kabbalistic ascription to Atziluth in some schemes, the fire tattva as an upward red triangle borrowed from Indian sources: each of these belongs to a named system and travels with it. The atlas records them as attributions within those systems and not as properties of fire, because the moment they are detached from their scheme they begin to contradict each other.
Sources The Golden Dawn: The Original Account of the Teachings, Rites, and Ceremonies of the Hermetic Order of the Golden Dawn, 6th editionIsrael Regardie with TetrabiblosClaudius Ptolemy