Gemara

97b: Some thighs were salted with the Gid ha'Nasheh inside. Ravina forbade them, and Rav Acha permitted them.

Question (Rav Acha, to Ravina): Do you forbid because Shmuel taught that salted food is like Rose'ach (boiling hot), and pickling is like cooking? Shmuel forbade the thigh only if it was cooked with the Gid. If it was roasted, it suffices to peel off the layer around the Gid!

Do not say that Shmuel said that salted food is like Rose'ach, i.e. like cooking. Since he said that pickling is like cooking, we infer that salting is not. Rather, it is like roasting!

This is left difficult.

104b (Abaye): We decree not to put fowl and milk on the same table lest they be put together in a hot pan.

Question: A Keli Sheni cannot cook!

Answer: We decree lest they be put in a Keli Rishon.

(Beraisa): "Asher Tevushal Bo" teaches about a pot in which Chatas was cooked (it must be broken if it is earthenware, or Merikah u'Shtifah (scouring and rinsing, to Kasher it) if it is of metal.

Question: What is the source for a pot into which boiling Chatas was poured?

Answer: We learn from "Asher... Bo Yishaver" - if it absorbed Chatas (in any way).

Shabbos 40b (R. Yitzchak bar Avodimi): Once, I wanted to warm oil in the bath water and anoint Rebbi with it. He told ne to put the (flask of) oil in water in a Keli Sheni (but not in the bath, for it is like a Keli Rishon).

Inference: A Keli Sheni does not cook.

Shabbos 42a (Beraisa - Beis Hillel): One may pour hot water into cold water, or vice-versa.

This refers to a cup. However, in a bath, one may put only hot into cold.

R. Shimon ben Menasiyah forbids.

(Mishnah): On Shabbos, if one removed a frying pan or pot from the fire, one may not put spices into it. One may put spices into a bowl (a Keli Sheni).

R. Yehudah says, one may put into any (food), except for one with vinegar or brine.

(Beraisa - R. Yehudah): One may put into any simmering pot or pan, except for one with vinegar or brine.

This shows that R. Yehudah discusses the Reisha (putting spices in a Keli Rishon off the fire. (Compared to the first Tana,) he is lenient.

Rishonim

Rif and Rosh (Pesachim 8b and 2:7): Kelim used for Chametz in a Keli Sheni, e.g. bowls, it suffices to pour boiling water on them in a Keli Sheni and wait until the Isur is purged. We learn from pots of Nochrim. Everything is Kashered the way it is used.

Poskim

Shulchan Aruch (105:2): The heat of a Keli Rishon that is Yad Soledes Bo cooks and totally forbids. The heat of a Keli Sheni does not cook. Some say that also, it does not emit (what is absorbed in the Keli), and it does not absorb (from its contents). Some say that it emits and absorbs, and forbids Kedei Klipah (the thickness of a layer that can be peeled off). It is proper to be concerned for this l'Chatchilah, but b'Di'eved it is permitted without peeling off a Klipah. It suffices to rinse.

Beis Yosef (DH v'Im): The Tur says that if Isur mixed with Heter and it is Yad Nichbis Bo (hot enough to scald the hand), it forbids like cooking. If he discusses a Keli Rishon, this is real cooking! If he discusses a Keli Sheni, even Yad Soledes Bo does not cook, like Tosfos (Shabbos 40b DH u'Shma) says! It seems that the Tur himself says so in OC 318. It is difficult to distinguish between cooking regarding Shabbos and regarding Isurim. I say that the Tur said so because Stam cooking is in a Keli Rishon on the fire. The Tur teaches that there is one law for a Keli Rishon on the fire, and after it was removed, and a Keli Sheni. It forbids like cooking only as long as it is Yad Soledes Bo. However, this is astounding. Tosfos wrote that since a Keli Rishon was on the fire, its walls are hot and it retains its heat a long time. Therefore, as long as Yad Nichbis Bo, it forbids. A Keli Sheni, even if it is Yad Soledes Bo, is permitted, since its walls are not hot, rather, they cool off. The Tur himself said so in OC! Rather, he discusses only a Keli Rishon. People think that it cooks only while it is on the fire, or after it was removed and it is still boiling like when it was on the fire, but not after it stops boiling. The Tur teaches that this is wrong. Even if it stopped boiling and it is off the fire, as long as it is Yad Soledes Bo, it cooks, like Tosfos said. I say that even if a Keli Sheni is boiling like a Keli Rishon, it does not cook. This is a great general rule that a Keli Sheni does not cook. The Gemara would not have said Stam that it does not cook if sometimes it cooks. However, below the Tur brings the Rashba, and says that a Keli Sheni forbids if it is Yad Soledes Bo. Therefore, it seems that the Tur discusses a Keli Rishon and Keli Sheni. As long as it is Yad Soledes Bo, even though it does not cook, it emits and absorbs.

Dagul me'Revavah: The Maharshal (8:64) says that a Keli Sheni emits or absorbs, but not both together. Therefore, if a dairy spoon Ben Yomo was put in a pot with meat and sauce, the spoon and sauce are forbidden (perhaps they absorbed), but the meat and pot are permitted (even if the spoon emitted its milk into the gravy, it would not be absorbed into the meat or pot).

Shach (5): If something is normally rinsed afterwards, one may put it on cold Isur. Here (in a Keli Sheni) one should be careful l'Chatchilah. The Rashbam holds that a Keli Sheni does not absorb at all. R. Tam and all who hold like him, including Semag, hold that a Keli Sheni is Mavli'a (causes its contents to absorb) Kedei Klipah. This is unlike the Maharshal said in Isur v'Heter (33). Semag says that even a Keli Cheres absorbs in a Keli Sheni, and all the more so food absorbs. Many Rishonim and Acharonim hold that it does not absorb at all; the Rema says so in Toras Chatas (33:1). However, in OC 451:1 the Rema connotes that a Keli Cheres used with Chametz in a Keli Sheni is forbidden! Perhaps this is a stringency of Chametz. In any case, one should forbid a Keli Cheres if it is not a big loss. The Ramban and Rashba hold that even a copper Keli (Sheni) absorbs. Some Poskim say that even though a Keli Sheni does not cook, it emits and absorbs. Similarly, one should peel a food if it is not a big loss. In any case we do not totally forbid in a Keli Sheni. In his Teshuvah, the Maharshal said that it absorbs only Kedei Klipah. Why did he totally forbid in Yam Shel Shlomo (8:71)? The Bach is stringent to say that a Keli Sheni emits and absorbs at once, and totally forbids. This is astounding. We are stringent to say that Iruy Keli Rishon forbids Kedei Klipah!

Gra (13): The Yerushalmi says that Chachamim made a fence for a Keli Rishon, but not for a Keli Sheni. A Keli Sheni does not cook even if it is Yad Soledes Bo.

Gra (13, Likut): The Rashba brought a proof from salting, which absorbs Kedei Klipah. This is not a valid proof, since salting is like intense heat of roasting. There was a Hava Amina that it is like cooking to totally forbid (Chulin 97b).

Gra (68:33): Chulin 104b proves that a Keli Sheni does not cook even if it is Yad Soledes Bo.

R. Akiva Eiger: If Kelim were used in a Keli Sheni, since one can Kasher them, one must do so l'Chatchilah. Klei Cheres are permitted (for this is b'Di'eved; one cannot Kasher them).

Shulchan Aruch (OC 451:1): One cannot Kasher for Pesach any Keli Cheres used for hot Chametz through heating it, even if it was not on the fire, only hot Chametz was poured into it.

Rema: Some forbid even in a Keli Sheni.

Beis Yosef (DH u'Mah she'Chosav Rabeinu): The Tur is stringent even for Kelim not used on the fire, rather, hot food was poured into them. I.e. even if it was used like a Keli Sheni, heating the Keli will not Kasher it. Also the Rambam equates a Keli Sheni to a Keli Rishon regarding Keli Cheres used for Chametz.

Darchei Moshe (1): The Magid Mishneh says that heating a Keli Cheres does not help, even if it was used only like a Keli Sheni. The Beis Yosef says that the Tur agrees. This is wrong. The Tur holds that absorptions occur only in a Keli Rishon or through Iruy, which is like a Keli Rishon.

Magen Avraham (3): The Beis Yosef omitted (from the Shulchan Aruch) this law (that a Keli Sheni of Cheres used for Chametz is like a Keli Rishon), because he retracted.

Rebuttal (Chak Yakov 13): Here, the Shulchan Aruch cites the Tur, for he forbids even a Keli Sheni. This is clear from what he wrote in Sa'if 5 (below), that a Keli used for Chametz in a Keli Sheni requires Hechsher in a Keli Sheni. He did not retract.

Defense (Machatzis ha'Shekel DH v'Chen): The Mechaber retracted, and forbids only through Iruy. We cannot prove this from the Rema, who says 'some forbid', for he often says so when the Mechaber is not clear. The Beis Yosef wrote that the Tur is like the Rambam, for there is no need to say that they argue. We can explain that the Tur forbids even a Keli Sheni. If the Mechaber intended to rule like this, he should have said clearly that a Keli Shares forbids, lest we think that it is only through Iruy. Rather, he retracted and forbids only through Iruy.

Gra (5 DH v'Yesh): The Rambam forbids Keli Cheres, because other Kelim must be Kashered. In Zevachim we say that absorptions do not depend on cooking. The Rif and Rosh bring so from the Yerushalmi. However, they discussed only Kelim used through Iruy; Iruy suffices to Kasher them. The Rosh says so in Pesachim. The Shulchan Aruch in Sa'if 5 is astounding. It is only according to the Rashba.

Mishnah Berurah (1): Also bowls used through Iruy and a Keli Sheni cannot be Kashered.

Mishnah Berurah (11): One should be stringent like the Rema. Even a Keli Sheni requires Kashering if it is metal, and may not be used if it is of Cheres. B'Di'eved, if a Keli Sheni was used without Kashering, one may be lenient, even regarding a Keli Cheres, if being stringent would cause a big loss or prevent Simchas Yom Tov, if it is not a Ben Yomo.

Kaf ha'Chayim (20): One may be lenient only if the Keli was clean. If not, any amount of Chametz during Pesach forbids a mixture.

Kaf ha'Chayim (18): If one poured into a bowl from a Keli Sheni, all permit the bowl.

Kaf ha'Chayim (19): This opinion holds that a Keli Sheni absorbs somewhat. This is why they need some Kashering, i.e. in a Keli Sheni (Shulchan Aruch Sa'if 5).

Shulchan Aruch (5): If Kelim were used for Chametz in a Keli Sheni, one Kashers them in a Keli Sheni. If one did Iruy over them from a Keli Rishon, he Kashers them through Iruy Keli Rishon. It is not enough to Kasher them in a Keli Sheni.

Kaf ha'Chayim (81): If one held a bowl in a Keli Rishon until the water in the bowl boiled, we are stringent to consider the bowl like a Keli Rishon, but perhaps we are not lenient to consider it a Keli Rishon to enable Kashering inside it (Taz 92:30, b'Sof).

Kaf ha'Chayim (84): Since we hold that a Keli Sheni absorbs Kedei Klipah, we are stringent about Chametz, since any amount of Chametz forbids (a mixture).