Insulating food Friday evening

The fourth perek of Shabbat (47b–51b) discusses hatmanah, insulating hot food on Shabbat. Materials that add their own heat may not be used. Why not?

Rava establishes on Shabbat 34a–b that there are two rabbinic decrees against hatmanah. One decree applies to insulating materials that add heat, which may not even be used from Friday going into Shabbat. The other decree applies to materials that insulate without adding heat, which may be used on Friday but not once Shabbat starts. The fourth perek then defines which materials add heat and which don't.

“A keli sheni cannot cook”

Disclaimer: nothing in this post should be taken as practical. As Rav Eliezer Melamed explains,

התשובה הכללית, שבכלי ראשון הדבר אסור ובכלי שני מעיקר הדין מותר, אולם בפועל רק בכלי שלישי מותר.

In general, even though putting food in a keli sheni is permitted in principle, in practice we often allow only a keli shelishi. This post discusses the principle, not the practice.

Why is a keli sheni different from a keli rishon? Isn't possible to have a keli sheni that is just as hot as a keli rishon and cooks food just as easily?

Leaving a pot right on the coals

The third perek of Shabbat starts by discussing a pot left on the stove as Shabbat begins (Shabbat 36b):

משנה. כירה שהסיקוה בקש ובגבבא - נותנים עליה תבשיל. בגפת ובעצים - לא יתן עד שיגרוף, או עד שיתן את האפר. בית שמאי אומרים, חמין אבל לא תבשיל ובית הלל אומרים, חמין ותבשיל. בית שמאי אומרים, נוטלין אבל לא מחזירין ובית הלל אומרים, אף מחזירין.

You may not “place” a pot on a stove fueled by peat/marc/pomace (Soncino/ArtScroll/Steinsaltz) or wood, unless you sweep away the coals (gerifah) or cover them with ash (ketimah). Rashi explains the reason as the general rabbinic prohibition against insulating, hatmanah, with something that adds heat. Rabbeinu Hananel and others disagree, and say that the shehiyyah in this mishnah is a unique decree distinct from hatmanah. To this latter opinion, hatmanah applies to a pot resting directly on top of the coals, whereas shehiyyah applies to a pot with legs so it stands above the coals.