La Genèse 34:25 Halakha : Mishneh Torah, Sabbath & Gray Matter II

We make a bonfire for a birthing woman even in the days of summer, since the cold is very difficult for a birthing woman in the cold areas. But we do not make a bonfire to warm an ill person. [However] if he let blood and got cold, we make a bonfire for him even during the season of Tamuz (the hottest part of the summer). And we bathe an infant on Shabbat on the day that it is born after we cut the umbilical cord – even with hot water that was heated on Shabbat. And we apply salt to him and give him a bone massage because it is dangerous if they do not do all these [things] to him. Likewise, we bathe him in hot water that was heated on Shabbat before circumcision, [right] after the circumcision and three days after the circumcision because of the danger.

When a brit milah (circumcision) takes place later than the eighth day of a boy’s life (such as a baby who could not tolerate a brit on the eighth day due to health reasons, or a non-Jew who wishes to convert),⁷Of course, none of these concerns applies when circumcising a baby on the eighth day of his life, as circumcision on the eighth day overrides Shabbat. The Gemara discusses the laws of a circumcision on Shabbat at great length in the nineteenth chapter of Masechet Shabbat. the Tashbetz (1:21) forbids performing it on a Thursday. He notes that on the third day after a brit (including the day of the brit), the baby is presumed to be in tremendous pain (see Bereishit 34:25 and Rashbam ad loc.). Thus, a baby who underwent a brit milah on Thursday may require medical treatment that will entail transgressing Shabbat (see Shabbat 86a). According to the Taz (Yoreh Deah 262:3), this problem exists when circumcising on Friday, too, as the baby suffers pain every day through the third day.⁸The Taz indicates concern for the baby’s pain and suffering per se, not for the desecration of Shabbat that it might necessitate. Apparently, he understands the problem of circumcising close to Shabbat in the same manner that the Rif explains the prohibition against traveling before Shabbat - concern for causing unnecessary discomfort during Shabbat (see Teshuvot Tzitz Eliezer 12:43). The Shach (Yoreh Deah 266:18) notes that some Rishonim do indeed assume that the baby suffers through the third day, but the Tashbetz explicitly permits circumcising on Friday even when it is not the eighth day.⁹See, however, Teshuvot Yabia Omer, Y.D. 5:23.