Yoma, Chapter 3, Mishnah 5. Our Mishnah begins by discussing the time of the burning of the incense on every day of the year, and then returns to the situation of the Kohen Gadol during his immersions on Yom Kippur.
"Ketores shel shachar hayesah kereivah bein hadam la'eivarim" - the morning incense was offered between the blood and the limbs:
The incense that was burned in the morning was offered between the sprinkling of the blood of the daily tamid offering and the placing of the limbs of the tamid on the altar. The incense served as a break between these two services.
The commentators raise a question here: in the previous Mishnah we learned that the order of the service was the sprinkling of the blood, then the incense, then the kindling of the two lamps, and only afterwards the placing of the limbs. If so, the incense was positioned between the sprinkling of the blood and the kindling of the lamps, and not between the blood and the limbs, since the limbs came in turn only after the kindling of the lamps.
The commentators explain that the Mishnah does not mean that the incense was offered precisely between the blood and the limbs; this is not meant literally. The main point being taught is that the sprinkling of the blood and the placing of the limbs were not performed one immediately after the other, but rather the incense came between them, and so too the kindling of the two lamps.
"Shel bein ha'arbayim - bein eivarim lanesachim" - that of the afternoon was offered between the limbs and the libations:
The incense that accompanied the afternoon tamid was offered after the limbs had already been brought, and before the libations - the meal offering, the oil and the wine libation, which were performed after the incense.
"Vehayah kohen gadol zakein o istenis" - and if the Kohen Gadol was elderly or delicate:
From here the Mishnah returns to the immersions of the Kohen Gadol and to the concern about the cold that was involved in them. Two situations are mentioned:
"Zakein" - a Kohen Gadol who was advanced in years.
"Istenis" - a delicate and sensitive person, for whom the difficulty of the cold is felt more acutely.
In such a case - "machamin lo chamin" - they would heat water before Yom Kippur and keep it from cooling off, so that it would remain somewhat warm. "Umetilin letoch hatzonein" - they would pour it into the cold water, "kedei shetafug tzinasan" - in order to reduce and remove the chill of the water, so that it would not be so cold for him at the time of his immersion.
The explanation of the Gemara:
The Gemara explains that it was not hot water that they placed into the cold water, but rather pieces of metal that had been heated before Yom Kippur and left on the fire until the next day. Before the Kohen Gadol went down to immerse, they would remove them from the fire and place them into the water.
Although at first glance this involves a shevus - a rabbinic prohibition - the rabbinic prohibitions of shevus were not enforced in the Beis HaMikdash, and many of the decrees of the Sages did not apply in the Temple.
In summary: In this Mishnah we learned the place of the incense within the order of the tamid service - in the morning, between the sprinkling of the blood and the placing of the limbs (though not literally adjacent, since the kindling of the lamps also came between them), and in the afternoon, between the limbs and the libations. We also learned about the leniency granted to a Kohen Gadol who was elderly or delicate, placing hot material into the cold water so that its chill would dissipate, and the Gemara's explanation that this was done by means of pieces of metal heated before Yom Kippur, since there is no shevus in the Beis HaMikdash.