Question:
You wake up on Shabbos morning and find the water on the blech is no longer hot ["yad soledes bo" about 110 degrees] but still warm - is it permitted to move it directly above the fire to heat it up and boil it?
Answer:
If there is any doubt as to whether it was hot [yad soledes bo] originally, then it is absolutely forbidden to move it. If originally it had been heated until yad soledes bo, but it cooled off a bit, lichtchila one should be strict and not move it but if necessary one may move it on the condition that on Erev Shabbos it was placed on the blech where it was yad soledes.
The reason is that if it wasn't originally hot then to heat it is bishul min ha-torah. If it was cooked originally then as long as it hasn't completely cooled off it is permitted to reheat [as the Rema says]. The problem is "chazara", namely, returning cooked food to the fire after it was removed. Even though it is still on the blech, it would seem to be a case where it is considered "off the fire" making it forbidden to return [unless one fill all of the conditions of chazara, such as having daas to return it to the fire when removing it].
If, however it was on the blech in a place where the water would be heated until yad soledes [and was moved afterwards so that the water doesn't dissipate] then one can put it directly on the fire. We can rely on the opinion of the Ran who says that the whole prohibition of chazara only applies when it was removed before Shabbos. In our instance, when it was in place when Shabbos started one would be permitted to do chazara. In addition there is a צורך גדול - a great need so that people can enjoy Shabbos more. We can also factor in the opinion that as long is it is still on the blech it is not considered chazara, even if it far from the fire. Also, if when he moved the water originally, he was under the assumption that it will remain very hot, we can apply the opinion of many Rabbis that if the gas extinguished on Shabbos [by itself] and the stove was completely cooled off, nevertheless it is permitted to return it to another fire since it wasn't removed from the fire on purpose. So too, if the removal was under false assumptions, he can return it [see Bitzeil Hachochma 4/ 137].
One should still be strict if possible.
[Based on Nishmas Shabbos 1/2 - see there for more]
לזכות כלב אברהם בן אלישבע