We see the figure in the card literally mixing two liquids; they could well be water and wine. To 'temper' is to act as a neutralising or counterbalancing force. Obviously if we put water into wine, this will dilute it, neutralising or counterbalancing its strength.
When the French say 'put some water in your wine,' they mean something like 'chill out' or 'take it down a notch'. This could be in a positive way, like being more tolerant or being willing to compromise, or in a not so good way, like lowering one's standards or 'selling out'. Usually, though, it's considered the best thing to have done in the situation. Going to extremes is almost never the best course of action.
If you put some water in the wine (or Scotch or bourbon), you make it milder and easier to drink. If you put some water in your wine metaphorically, you make yourself milder and more palatable. :)
In fact, being able to 'put water in one's wine' is clearly a blessed ability, resulting in seeming miracles, because the figure in this card appears to be some sort of angel, having wings and a flower on her forehead (third eye? crown chakra?), and performing the impossible by pouring liquid horizontally. That's a pretty neat trick!
The neat trick of 'putting water in one's wine' is a completely internal process, as seen in the card. The lone figure stands completely enrobed, her garments are heavy and cover her completely. The liquid she pours goes from one vessel to the other, all her own; it is not poured out onto the ground or into a stream or bowl that others might access. As Yoav Ben-Dov points out in The Open Reading, she is 'rooted to the ground, and the raised elbows may be fending off other people from invading [her] personal space.' He goes on to say, 'This can indicate excessive preoccupation with oneself and with one's own inner processes, which leaves no place for practical advancement or close contact with others.' Which is kind of interesting -- can Temperance itself be intemperate?? I guess that's its shadow side! 'Going back and forth without making real progress,' as Ben-Dov puts it. I never thought of that as in interpretation of the pouring back and forth action of Temperance!
How could you be more temperate today? Do you need to put some water in your wine somewhere in your life? How might you be going back and forth without making real progress?