The Shulhan Aruch (Orah Haim 325:11) rules that just as one may not benefit from a Melacha (forbidden activity) that a gentile performs for a Jew on Shabbat, it is likewise forbidden to benefit from a Melacha which a gentile performed for both himself and a Jew. For example, if a non-Jew heats water on Shabbat with the intention that both he and a Jew will use the hot water for tea or coffee, Jews may not use this hot water on Shabbat.
On the basis of this ruling, the Aruch Ha’shulhan (Rav Yechiel Michel Epstein of Nevarduk, 1829-1908) presents a scathing condemnation (in 325:11) of certain wealthy Jews who used the hot water prepared on Shabbat by their non-Jewish housekeeper or butler. These Jews claimed that since the non-Jew would also be using the hot water, it was permissible for them, as well. The Aruch Ha’shulhan sharply criticizes this claim, charging that it was an attempt to deceive G-d, Heaven forbid, as the housekeeper clearly intended to heat the water for the entire household, just as he or she did throughout the week. Such dishonesty, the Aruch Ha’shulhan writes, amounts to "Hutzpah Kelapeh Shemaya" – a display of audacity towards G-d. The Aruch Ha’shulhan laments the fact that some of these Jews even instructed the non-Jew to lie and say that the water was boiled only for himself or herself.
Moreover, the Aruch Ha’shulhan adds, even if it were true that the gentile housekeeper heated the water only for herself, the Rabbis enacted a provision forbidding drinking from such a pot. If Jews were allowed to use hot water heated by a gentile for himself on Shabbat, the gentile might then heat water for a Jew the next Shabbat, or add more water the next Shabbat for the Jew, and the Jew would use that hot water, in violation of Halacha.
The Aruch Ha’shulhan concludes his discussion by warning that using the hot water heated by the non-Jewish housekeeper for the family constitutes a very grievous sin, and that those who avoid this sin are worthy of blessing.
Therefore, one must ensure that the hot water urn was set up before Shabbat, and that the housekeeper did not heat the water or add water on Shabbat.
Summary: If a non-Jewish housekeeper heats water in an urn on Shabbat, or adds water to an urn on Shabbat, a Jew may not use this hot water on Shabbat, such as to make tea or coffee, even if the housekeeper heated the water also for herself. One may use hot water from an urn on Shabbat only if the urn was set up before Shabbat.