Is it permissible to fill an urn with cold water just before the onset of Shabbat, such that the water will be heated on Shabbat?
Halacha imposes certain restrictions on placing raw or partially cooked food on the fire before Shabbat. The Rabbis were concerned that since the food is not fully cooked when Shabbat begins, one might stoke the coals to expedite the cooking process, which would constitute a Shabbat violation. Accordingly, these prohibitions apply only in cases where there is the possibility of accelerating the cooking process. Hence, according to most authorities, if an urn has no dials or knobs, and is simply plugged into the wall, one would be allowed to fill it with cold water just before the onset of Shabbat, since he has no possibility of increasing its heat to accelerate the cooking process on Shabbat.
Rabbi Moshe Feinstein (Russia-New York, 1895-1986), in his sefer Igrot Moshe, Helek 4, Siman 74:23, however, ruled stringently on this issue, forbidding filling an urn with cold water if the water will not become hot before the onset of Shabbat. He was concerned that a person may take some water from the urn before the water is fully heated, which will have the effect of accelerating the heating process, as a lower quantity of water heats more rapidly than a higher amount. Rabbi Feinstein felt that due to this concern we should forbid filling an urn just prior to Shabbat.
The majority of authorities, however, disputed this ruling, arguing that the Talmud makes no mention of such a concern. It speaks only of the concern that one might stoke the coals, and therefore in situations where there is no possibility of increasing the heat to accelerate the heating process, one may fill an urn with cold water just prior to Shabbat. See Sefer Matmin U’Mevashel BeShabbat, page 44.
Summary: One may fill an urn with cold water just before Shabbat, even though the water will still be cold when Shabbat begins, provided that the urn has no dials or knobs for adjusting its heat.