Temperance began as one of the four cardinal virtues and ended up as something considerably stranger, and the change is traceable.
The fifteenth-century card is a straightforward personification: a figure, usually winged, pouring liquid between two vessels. Temperance in the medieval sense is not moderation in the modern weak sense of doing less; it is the correct mixing of things, and the standard image for it is diluting wine with water. That is what the vessels are for. The virtue is proportion.
The occult tradition read the pouring differently. Once the tarot had been attached to alchemy, a nineteenth-century move, not a fifteenth-century one, the two vessels became the combination of opposed substances, the figure became an angel presiding over a work, and the card became about synthesis rather than restraint. The Golden Dawn assigned it the letter Samekh, the sign Sagittarius, and the twenty-fifth path from Tiphareth to Yesod, which in that system is the path of the arrow shot upward through the middle of the Tree, and gave it the alchemical title Art. Crowley kept that title for his own version.
So the card carries two readings that are almost opposites in emphasis. One counsels not overdoing it. The other counsels combining two things that do not obviously go together and standing over the mixture while it works. Both are in use, and a reader who knows only the first will find the card oddly weak in spreads where the second is what is happening.
The historical point worth holding onto is that the alchemical reading was applied to the card rather than found in it. Nothing connects the fifteenth-century virtue to the laboratory except the shared image of pouring, and the connection was made by nineteenth-century writers who were reading both traditions at once and were pleased to find them agreeing.