Gemara

20a - Mishnah: If limbs (of an Olah) flew off the Mizbe'ach before midnight we return it; Me'ilah applies to it. If it flew off after midnight we do not return it, and Me'ilah does not apply.

Question: What is the source of this?

Answer (Rav) Contradiction: The Olah should burn "Al ha'Mizbe'ach Kol ha'Laylah". The verse continues "V'Herim" (at night it may be taken off the Mizbe'ach)!

Answer #1 (Rav): We divide the night into two halves. The first half is for Haktarah, the latter is for Haramah.

Objection (Rav Kahana - Mishnah): Normally, Terumas ha'Deshen is done at Kros ha'Gever, or slightly before or after it. On Yom Kipur it is done after midnight. On the festivals, it is done after the end of the first Ashmores (third of the night).

If mid'Oraisa the first half is for Haktarah, we could not do Terumas ha'Deshen before midnight!

Answer #2 (R. Yochanan) Question: "Kol ha'Laylah" connotes until morning. Why does it also say "Ad Boker"?

Answer: This teaches that there is another 'Boker' (during the night that is a transition from Haktarah to Haramah).

Rashi (DH Ela): R. Yochanan answers that Kol ha'Laylah is Kosher for Haktarah (of limbs not yet consumed), and also for Haramah (removal) of ashes. The additional 'Boker' causes burned limbs (which are not yet ashes) to be considered consumed; the Torah did not specify the time, so it must be midnight. The Torah did not fix the time for Terumas ha'Deshen; Chachamim fixed the time according to needs of the day.

27b - R. Zeira: A Zar is Kosher for any Avodah Kosher at night.

Question: A Zar is Pasul for Terumas ha'Deshen, even though it is Kosher at night!

Answer: Terumas ha'Deshen begins the coming day's Avodah:

R. Yochanan: If a Kohen was Mekadesh for Terumas ha'Deshen, he need not Mekadesh again the next day, because Terumas ha'Deshen begins the coming day's Avodah.

Zevachim 20a: R. Yochanan holds like Rebbi, who says that the obligation to be Mekadesh again in the morning is only mid'Rabanan. Chachamim do not obligate one who was Mekadesh after Kros ha'Gever (it appears like the coming day).

Yoma 27b - R. Yochanan: If a Zar arranged two logs on the Mizbe'ach he is liable, for this is a daytime Avodah.

Megilah 20b - Mishnah: Haktaras Chelev and Eimurim is Kosher the entire night.

Tamid 28b - Mishnah: (After Terumas ha'Deshen) Kohanim took pitchforks to move limbs and Chelev that were not burned to the sides of the Mizbe'ach. If there was not room on the sides, they put them on the ramp near the Sovev.

Rishonim

Rambam (Hilchos Temidim u'Musafim 2:11): Normally, Terumas ha'Deshen is done at dawn. On the festivals, it is done after the first Ashmores. On Yom Kipur it is done after midnight.

Question: The Mishnah says that normally, Terumas ha'Deshen is at Kros ha'Gever, or slightly before or after it!

Answer #1 (Radvaz): Dawn is slightly after Kros ha'Gever.

Answer #2 (Lechem Mishneh): Perhaps the Rambam holds that Kros ha'Gever is dawn.

Question: Zevachim 20a says that Kros ha'Gever is before morning!

Answer #1 (Likutei Halachos Yoma 6b Ein Mishpat 200): The Rambam means that Terumas ha'Deshen was slightly before dawn, like he says in Perush ha'Mishnayos (Tamid 1:2).

Answer #2 (Gilyon ha'Rambam of R. Akiva Eiger): The Rambam (Bi'as Mikdash 5:9) holds that 'morning' (that requires another Kidush) is not dawn, rather, sunrise.

Question: A Mishnah (Megilah 20b) teaches Avodos that are Kosher the entire night. Why does it not mention Terumas ha'Deshen?

Answer #1 (Tosfos 20b DH Ela): This is because Terumas ha'Deshen was never done before the end of the first Ashmorah.

Answer #2 (Tosfos R. Akiva Eiger on Mishnayos Megilah (25)): Terumas ha'Deshen is also Kosher during the day, therefore the Mishnah omitted it. This is like the Rambam, but Tosfos (27b DH Ika) holds that Terumas ha'Deshen must be at night (like we learned (20a) from "Kol ha'Laylah...v'Herim").

Mefaresh (to Tamid 28b DH Sodrin): Even if the limbs and Chelev are on the ramp, they are considered to be on the Mizbe'ach, so Linah does not apply. Therefore, they may be returned later to the Ma'arachah.

Shoshanim l'David (2:1 DH Tosfos Yom Tov): This implies that Terumas ha'Deshen is before dawn, for after dawn there is no concern for Linah! We also learn this from Yoma 27. Also, there were lotteries and Avodos after Terumas ha'Deshen but before Shechitah of the Tamid, which is at He'ir ha'Mizrach (when the eastern sky is lit up).

Question: The Rambam says that Terumas ha'Deshen was after dawn!

Answer #1 (Avodas Yisrael): The Rambam holds that between dawn and sunrise is night.

Rejection (Shoshanim l'David, ibid.): The Rambam (Avodas Yom Kipur 1:8) says that we do not slaughter the Tamid until it is clearly after Amud ha'Shachar, lest one slaughter it at night.

Answer #2 (Avodas Yisrael): The Rambam says that Terumas ha'Deshen is 'mishe'Ya'aleh ha'Shachar'. This means before Amud ha'Shachar.

Answer #3 (Shoshanim l'David, ibid.): The Rambam teaches that Terumas ha'Deshen is Kosher even after dawn.

Question (Tosfos Sukah 51b DH Kara): After Kros ha'Gever they went to draw water for Nisuch ha'Mayim. Indeed, Kidush of hands and feet is not disqualified after Kros ha'Gever, but Kodshim become Pasul through Linah at morning!

Answer (Tosfos, ibid.): They would delay putting the water in a Kli Shares until dawn. Linah does not apply before Kidush in a Kli Shares.

Maharsha: Maharshal explains that Kros ha'Gever is dawn, and Linah applies at morning, i.e. sunrise. This is wrong. Rather, Kros ha'Gever is before dawn, and Linah applies at dawn.

Aruch l'Ner (Sukah 51b DH Kora): Rashi holds like the Maharsha, and it appears that Tosfos also does. The Rambam hold like the Maharshal.

Poskim

Shulchan Aruch (OC 1:6): Parashas ha'Korbanos should be said only during the day.

Magen Avraham (6): One may say Parshiyos ha'Kiyor and Terumas ha'Deshen at night, for they are Kosher at night.

Objection (R. Akiva Eiger): Parashas Terumas ha'Deshen includes "U'Vi'er ha'Kohen Aleha Etzim" (Vayikra 6:5), and the two logs must be during the day!

Answer (Pri Megadim 10): Even though it says "Ba'Boker ba'Boker", Tevu'os Shor says that the logs may be placed at night. The Rambam says that they are placed during the day, and that l'Chatchilah Terumas ha'Deshen is after dawn.

Mishnah Berurah (17): If one will not have time to say Parashas ha'Korbanos after it is day, he may say it before day.