Closing the debate between Ben Zoma and R. Yehudah, not wholly satisfactorily. The washing sanctification and the immersing was all done in a holy chamber near the kohen's chamber -- except for the first immersion of the day, which took place outside, in the water that arrived to the Temple via an aqueduct higher than the courtyard of the Temple. Also, a new mishnah! Continuing with the procedures of the day. Beginning with the kohen gadol's wardrobe change, more washing, and the Korban Tamid of the morning, shared with another kohen/other kohanim. Plus a Korban Minchah, more with blood, and the incense of the morning... and afternoon. [What's What: Istanis (again)] They would adjust the temperature of the mikveh, if the kohen gadol was sensitive to the temperature. The Gemara here responds to his human need.