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This question is related. The difference here is that there is a delay between adding the water and the element coming on.
On Yom Tov there is insufficient water in the urn.
A small amount of cold water can be added to the urn without tripping the thermostat. A large amount of water causes the main heating element to come on but not immediately, only after say 30 seconds or one minute.
Is there any source which gives permission to add the large amount of water?
It's permissible. The reason is because even if you hold that electricity has the same status as fire regarding the 39 prohibitions of shabbat, on yom tov making a fire from scratch is only a rabbinic prohibition under the category of nolad. (Making a new entity come into existence). So we are dealing with a rabbinic prohibition, however since in your case it would take approximately 30 seconds till it is activated, this is known as GRAMA. (Indirect affect of an action). So now we have something called a shvus dshvus, which means the rabbinic prohibition is done in a rabbinic fashion. Which is permissible in this case.
