It occasionally happens that food that was left on the fire or hotplate on Shabbat becomes dry, and one wishes to add water to the pot to moisten the food. Is this permissible on Shabbat?
The pot in which food had been cooked on the fire, which is called a "Keli Rishon" ("first utensil"), is considered capable of Halachic "cooking" even after it is taken off the fire. Meaning, while the food is in the original pot in which it had been cooked, it can have the effect of Halachically "cooking" food or liquid poured into it. Therefore, it is clear that one may not pour cold water into the pot on Shabbat, even after it is taken off the stove or hotplate, as this will have the effect of cooking the water.
One might have assumed that pouring hot water into the pot directly from an urn or kettle should be permissible. Since the water is already hot when it enters the pot, no cooking takes place, and it should therefore be allowed on Shabbat. Rabbenu Yona, however, in his Iggeret Teshuba, writes that this is incorrect. For one thing, he notes, often people mistakenly think the water in the kettle is still hot when in fact it has already cooled. But additionally, even if the water is hot, once it exits the kettle into the air it cools somewhat, and then becomes reheated when it enters the pot. Therefore, Rabbenu Yona rules, it is forbidden to pour even hot water into a pot of hot food on Shabbat. This is also the opinion of many other Rishonim, and is the position taken by the Shulhan Aruch (253:4; listen to audio recording for precise citation). Although Ashkenazim do not follow this ruling, Hacham Ovadia Yosef writes (listen to audio recording for precise citation) that Sephardim are bound by the Shulhan Aruchs position, and may not add water to a pot of hot food on Shabbat.
Hacham Ovadia adds, however, that if one transfers the food into another utensil, he may then add even cold water to the food. Once the food is contained in a "Keli Sheni" ("second utensil"), it is no longer capable of "cooking" in the Halachic sense, and water may thus be added at that point.
Summary: One may not add hot or cold water into a pot of hot food, even if the pot had been taken off the fire, as long as the food is in the pot in which it was cooked. Once the food is transferred to a different utensil, one may add hot or cold water.
