Shabbat 134 - Washing the baby
In the time of the Talmud it was customary to bathe the infant in hot water, before and after the circumcision, and failure to do so was considered potentially dangerous to the infant's life. Therefore, the Sages permitted washing the baby with hot water, even though normally this is forbidden. Some say that even if the water was warmed on Shabbat itself, the washing is still permitted. However, it has to be done in an unusual manner, by splashing the water with a hand. Even pouring it from a vessel is not considered a sufficient deviation.
Moreover, the third day of the sickness is considered the hardest, and accordingly Rabbi Elazar ben Azaryah permits washing the baby on Shabbat if this is the third day after the circumcision - because in the incident of Shechem " on the third day they were in pain ." This, however, is not a complete proof but only a hint: perhaps on the third only the adults are in pain, because they heal slowly, but to infants, who heal faster, it does not apply.
Art: John Adam P. Houston - Washing The Baby