In our city there are many power cuts. If you have an urn that has boiling water on shabbos and then there is a power cut and the water cools down. Then the power goes on again and heats up the water. Is that ok ?
If the water will get cold then essentially it is a problem of sheiya, leaving uncooked food on the fire on shabbos. (Chazara is not an issue here because you did not never took the water off the fire, and even though it cooled you did not make the fire and cook it, so bishul and maaseh shabbos is also not an issue.)
Therefore if the urn, doesn’t have adjustable settings, then shehiya isn’t an issue, and you could use the water. However if the urn has adjustable setting then tape should be placed over the settings.
Orchos Shabbos 2-15&18, Halachos of Shabbos (R’ Eider zt”l) ftnt 685, Piskei Teshuvos 254 -1.