Question:
If you have a pot of water on the blech, not directly above the fire and no longer boiling, but it is still hot enough that "Yad Soledes Bo" ["to scald a baby's stomach" - most poskim hold that this is about 110 degrees], is it permitted to push it on top of the fire [on the blech, of course] on Shabbos in order that it should boil?
Answer:
If on Erev Shabbos it was already boiling then according to the strict letter of the law one may push it on top of the fire [but one should be machmir not to]. If it was not boiling before Shabbos one may not push it on top of the fire.
Even though we pasken that it is permitted to "recook" water if it hasn't totally cooled off [אין בישול אחר בישול בלח בעודו חם אם לא נצטנן לגמרי] and it is considered "cooked" [as far as the prohibition of cooking is concerned] if it is yad soledes bo [Shulchan Aruch 318/14], nevertheless, the Tehilla Li'dovid [318/17] isn't sure about water that is set aside for drinking. It could be that if it wasn't boiling before Shabbos it is not considered "cooked". This is similar to food that was partially cooked on Erev Shabbos [כמאכל בן דרוסאי] which one is prohibited from cooking on Shabbos [see Mishna Brura 318/26 and Shaar Hatziyun 37 and Shu"t Minchas Yitzchak 10/ 28] So in our case, if it hadn't boiled before Shabbos, then it is forbidden to do so on Shabbos. [See Shmiras Shabbos Ki-hilchaso 1/96].
However, the Shvisas Shabbos [in the preface] was lenient. So was the first Lubavitcher Rebbe [Shulchan Aruch HaRav 318/9] and the Chazon Ish [so both chasidim and misnagdim have a solid anchor for leniency... ]. But since we are dealing with a di-orasia one should be strict.
If water was in an urn and before Shabbos it wasn't boiling, it would seem that one shouldn't remove water, because the remaining water will boil. However, one can argue that it is permitted because it would be a grama and possibly only a di-rabbanan according to those opinions that once it was partially cooked [yad soledes bo] it is considered cooked.
If the water was boiling before Shabbos then one can be lenient to push it on top of the fire [on the blech] even if it is now no longer boiling [but is still hot]. Similarly, one is allowed to return a pot of food to a different fire than it was taken from [חזרה מכירה לכירה] even though the second fire might be hotter.
[Based on the Nishmas Shabbos Vol. 1 Siman 1 עיי"ש]
לזכות ר' יוסף עזרא בן אסתר הוא ביתו וכל אשר לו ברכה בהצלחה בגשם ורוח