Where does the concept of a Kli Shlishi come from?

Question

When it comes to cooking on Shabbos, most people hold that things that are not allowed to be put in a Kli Sheni (a vessel once removed from the vessel that was on the fire) because it is considered cooking are able to be put in a Kli Shlishi (a vessel once removed from the Kli Sheni).

(See here for a short summary of these laws).

The Mishna Berurah (318:47) quotes the Pri Megadim who differentiates between a Kli Shlishi over a Kli Sheni.

The Pri Megadim (Ashel Avraham 318:35) quotes the BaCH who says that there is no difference between a Kli Sheni and a Kli Shlishi, and even a Kli Revi'i is considered like a Kli Sheni. He then says that with regards to tea, When one pours from "ממים טמונים‬" (which I'm interpreting to mean A Kli Rishon that was removed from the fire and kept warm through Hatmana, not if it was still directly on the fire - please correct me if I'm wrong) into a Kli Sheni, and from there into smaller containers, one can be lenient.

However, the Chazon Ish ( Orach Chaim, end of Chapter 52) says that he did not find a source to differentiate between a Kli Sheni and a Kli Shlishi and as long as the contents of the Kli Sheni are hot, pouring it into a Kli Shlishi doesn't change anything.

What is the source for a Kli Shlishi? If the Chazon Ish couldn't find a source for the difference, where do the Poskim that do differentiate get it from?

Somebody once told me that a Kli Shlishi is not mentioned in the Gemara or Shulchan Aruch. Is this true? If so, when was the concept introduced?

Answer 1

See here for what appears to be the Halachah of making tea or coffee with Keli Sheni and Keli Shelishi on Shabbath according to Lubavitch Pesak.

It seems the Mishnah Berurah and the Alter Rebbe both had similarities and differences of opinion on the matter, which are laid out in the sources cited. I think the article reflects a lenient interpretation of the Mishnah Berurah (Keli Sheni being ok); but I believe the idea of Keli Shelishi is consistent with Shemirath Shabbath KeHilchatha, which (the latter) I have relied upon for making coffee and other things with a Keli Shelishi.

Let me point out, anecdotally, though, that a Keli Shelishi, even if warm, does not allow the Keli Sheni liquid to remain Yad Soledeth Bo. At least in my experience. In fact, it takes me a very long time to dissolve instant coffee in such water. It might be different, however, if the initial water is at or near the boiling point (how one would maintain that, I do not know); my water is drawn from an urn, which I believe are generally between 160-180F.