Gemara

Beraisa - R. Yehudah: They would heat up Asasiyos (thick pieces of iron) before Yom Kipur and put them in the water on Yom Kipur (in which the Kohen Gadol would immerse) to blunt the chill.

Question: This is Metzaref (solidifies the metal, which is forbidden on Yom Tov)!

Answer #1 (Rav Bivi): The iron was not so hot that the water would be Metzaref it.

Answer #2 (Abaye): We can even say that it was hot enough for Tziruf. Since they do not intend for Tziruf, it is Davar she'Eino Miskaven (an action which may result in a transgression for which one does not intend).

Question: Abaye contradicts himself!

Beraisa - R. Yoshiyah: "(Yimol) Besar Orlaso" - one circumcises even if it will cut off Tzara'as (even though this is normally forbidden).

Question: Why is a verse needed to permit? One intends just to circumcise, not to cut the Tzara'as. Davar she'Eino Miskaven is permitted!

Answer (Abaye): R. Yoshiyah holds like R. Yehudah, who forbids Davar she'Eino Miskaven. (This shows that Abaye holds that Davar she'Eino Miskaven is normally forbidden!)

Answer: Abaye forbids Davar she'Eino Miskaven regarding mid'Oraisa Isurim, but not regarding Tziruf, which is only mid'Rabanan.

Shabbos 41a - Mishnah: If one cleared a kettle, one may not put water in it to get hot, but one may put water in it or in a cup to become lukewarm.

Question: What does this mean?

Answer #1 (Rav Ada bar Masnah): If one cleared (emptied) the water out of a kettle, one may not put a small amount of water in it to get hot, but one may put much water in it to become lukewarm.

Question: Putting cold water in hot metal is Metzaref!

Answer: He does not intend to be Metzaref. The Mishnah is like R. Shimon, who permits Davar she'Eino Miskaven.

Objection (Abaye): The Mishnah does not say that he cleared out of a kettle, rather, he cleared a kettle!

Answer #2 (Abaye): If one cleared a kettle (off a fire), one may not put a small amount of water in it to get hot, but one may put much water in it to become lukewarm. If one emptied the water out of a kettle, one may not put water in it at all, for it is Metzaref.

The Mishnah is like R. Yehudah, who forbids Davar she'Eino Miskaven.

Rav: It is permitted to put water in it to become lukewarm, but not (in order) to be Metzaref.

Shmuel: It is permitted even to be Metzaref.

Objection: Surely, one may not intend to be Metzaref!

Correction: Rather, Rav permits only a Shi'ur of water which will become lukewarm, but not a Shi'ur to be Metzaref. Shmuel permits even a Shi'ur to be Metzaref.

Inference: Shmuel holds like R. Shimon (who permits Davar she'Eino Miskaven).

74b - Rav Acha bar Rav Avira: If one put a wet peg into an oven to dry, he is liable for cooking.

One might have thought that he intends only to harden it. Rav Acha teaches that this is not so. He intends to soften it first (and he is liable for this), then it hardens.

Rishonim

Rif and Rosh (Shabbos 19b and 3:13) explain the Mishnah like Abaye. I.e., if one cleared a kettle off a fire, one may not put a small amount of water in it to get hot, but one may put much water in it to become lukewarm. If one emptied the water out of a kettle, one may not put water in it at all, for it is Metzaref.

The Mishnah is like R. Yehudah, who forbids Davar she'Eino Miskaven.

Rav: Only a Shi'ur of water which can Metzaref is forbidden. A Shi'ur which will become lukewarm is permitted.

Shmuel: Even a Shi'ur to be Metzaref is permitted.

This is like R. Shimon.

Rambam (Hilchos Shabbos 12:1): Heating up iron to be Metzaref it in water is a Toldah of burning. One is liable for this.

Source (Magid Mishnah): If one was not liable for it, they could have done it on Yom Kipur (they would not have needed to heat it from before Yom Kipur), because Ein Shevus b'Mikdash.

Rebuttal (Ra'avad): It is a Toldah of cooking, just like putting a wet peg into an oven to dry (for he intends to soften it first - Shabbos 74b).

Answer #1 (Magid Mishnah): Since the iron becomes (like) fire and can burn other things, it is a Toldah of burning, not of cooking. The Gemara calls a metal coal 'fire'.

Answer #2 (Avnei Nezer OC 1:229:9,11): The Rambam (9:6) agrees that heating metal to make it a coal it is a Toldah of cooking. The Ra'avad holds that if it would be a Toldah of burning, there would be no source that it is (also) a Toldah of cooking.

Answer #3 Chazon Ish (Moed 50:9 DH Kosav): The Rambam agrees that heating metal to soften it so he can shape it is a Toldah of cooking. However, heating metal to be Metzaref it is not cooking (because he does not need to soften it), rather, burning.

Rambam (ibid. 2): One who extinguishes a metal coal is exempt. If he intended to be Metzaref he is liable, for this is the Melachah of iron forgers. They heat up iron until it glows like a coal, then they extinguish it in water to forge it. One is liable for this Tziruf for it is a Toldah of extinguishing.

Rebuttal (Ra'avad): Putting a metal coal in water is not extinguishing (mid'Oraisa), but it is Makeh b'Patish, for this completes the forging. In any case he is exempt because Tziruf is mid'Rabanan.

Question (Tosfos Shabbos 41b DH Meicham): Rashi (Yoma 34b DH b'Chol) says that R. Yehudah permits Davar she'Eino Miskaven regarding Tziruf, for it is only mid'Rabanan (the text there should not say 'because Ein Shevus b'Mikdash'). If so, why does R. Yehudah (Shabbos 42a) forbid to extinguish a metal coal to avoid harm to the Rabim? And why does he forbid dragging a bed on dirt floor? Even if he makes a furrow, this is ki'Le'acher Yad, which is only mid'Rabanan!

Answer #1 (Tosfos, ibid.): Tziruf is mid'Oraisa. However, R. Yehudah forbids Davar she'Eino Miskaven only mid'Rabanan, therefore the Gemara in Yoma calls it mid'Rabanan, and permits because Ein Shevus b'Mikdash.

Note: Many texts of our Gemara say that R. Yehudah permits because Ein Shevus b'Mikdash. Rashi deleted this from the text.

Tosfos (Yoma 34b DH Rebbi): Regarding Shabbos R. Yehudah holds that Davar she'Eino Miskaven is only mid'Rabanan, because it is not Melachah Machsheves.

Answer #2 (Magid Mishnah): In Yoma, Abaye says that Tziruf is only mid'Rabanan. The Halachah follows Rav Bivi, who says that it is mid'Oraisa.

Answer #3 (Ramban Shabbos 42a DH Mechavin): Tziruf is mid'Oraisa only if one intends to make a Keli.

Answer #4 (Piskei Rid Yoma 34b DH Im): Here Tziruf is mid'Rabanan because later the iron will be put into fire to make a Keli.

Answer #5 (R. Chananel (Shabbos 42a DH Lemeimra) and BaHaG): R. Yehudah always forbids Melachah she'Einah Tzerichah l'Gufah. Shmuel permits it only to prevent damage to the Rabim (perhaps it is considered Piku'ach Nefesh), like he permits trapping snakes. A metal coal is dangerous even when it ceases to be red, so people do not know to beware; a wooden coal is dangerous only while it is glowing, and people know to avoid it then.

Ramban (ibid.): BaHaG and R. Chananel hold that Tziruf is always mid'Oraisa. In Yoma it is called mid'Rabanan because the iron made the water warm; Tziruf requires cold water.

Answer #6 (Rashba Shabbos 42a DH Gacheles): All Tziruf is mid'Rabanan. Even R. Yehudah permits in order to avoid harm to the Rabim.

Rambam (ibid. 22:6): If one emptied hot water out of a kettle, one may put cold water in it to make it lukewarm.

Magid Mishnah: Even though Abaye used the text of the Mishnah to refute this (Rav Ada's) explanation of the Mishnah, the law is true.

Kesef Mishneh: Even though Perush ha'Mishnayos explains the Mishnah like Abaye, the Rambam retracted and explains like Rav Ada. Abaye's question is not strong enough to justify establishing a Stam Mishnah like R. Yehudah, for the Halachah follows R. Shimon regarding Davar she'Eino Miskaven.

Rambam (Avodas Yom Kipur 2:4): If the Kohen Gadol was old or sick they would warm up pieces of iron from before Yom Kipur and on Yom Kipur put them into the water (in which he would immerse) to blunt the chill, for Shevus is permitted in the Mikdash. Alternatively they would mix warm water into the Mikveh until the chill was blunted.

Question: The Rambam permits Davar she'Eino Miskaven. Why does he attribute the Heter to Ein Shevus b'Mikdash?

Answer (Lechem Mishneh): Even though it is not a Pesik Reishei that putting water into a kettle will Metzaref, the Rambam holds that regarding the iron bars used on Yom Kipur it is a Pesik Reishei. A support for this is that the Gemara compares this to Milah of Tzara'as, which is a Pesik Reishei.

Poskim

Shulchan Aruch (318:12): If one removed hot water from a kettle he may put in (much) cold water to warm the water.

Gra (DH Meicham): The Shulchan Aruch explains like Rav Ada because Rav and Shmuel hold like him.

Beis Yosef (DH Meicham): The Ran says that it is not a Pesik Reishei, for perhaps the pot was not hot enough for Tziruf; the water that was inside keeps the pot from getting too hot. The Magid Mishnah says that the Rambam is Mechayev for a Pesik Reishei of Metzaref only if he intended. If not, there is no Melachah at all, for he did not intend to make a Keli!

Rebuttal (R. Akiva Eiger on Magen Avraham 36): The Lechem Mishneh (Shabbos 12:1) proved that the Magid Mishnah discusses extinguishing a metal coal, but not a Keli.

Mishnah Berurah (80): It is permitted when he does not intend for Tziruf, for it is not a Pesik Reishei. If he did intend, some say that he is liable mid'Oraisa.

Bi'ur Halachah (316 DH v'Lachen): The Taz (3) permits to close a box without checking whether or not there are flies inside (that will be trapped). Since he is unsure, this is Davar she'Eino Miskaven. This is a Chidush! Even though the current situation might dictate that a Melachah will definitely be done, it is permitted. The Ramban supports this. He says that Tziruf is not a Pesik Reishei, for perhaps the water was not hot enough; and perhaps the metal already was Nitzraf.