The Mishna in Masekhet Para (3:1) teaches that when the time came to slaughter and burn the para aduma for the purpose of preparing the purifying waters, the kohen assigned to burn the cow would spend a week away from home in a special chamber in the area of the Beit Ha-mikdash. In order to ensure that he would be in a state of tahara (purity) as required for the performance of this ritual, the kohen was required to remain in this chamber, where he would not be exposed to tum’a (impurity). The Gemara infers this law from the Torah’s account in Sefer Vayikra of the seven-day miluim procedure, whereby Aharon and his sons were formally consecrated as kohanim. They were instructed to spend the entire seven-day period in the courtyard outside the Mishkan (Vayikra 8:33), and they were told, “As was done on this day, the Lord commanded to do to atone for you” (Vayikra 8:34). The Gemara interprets this vague verse as a reference to two other occasions when a kohen was required to spend seven days in the Beit Ha-mikdash – the kohen gadol before Yom Kippur (Yoma 2a), and the kohen who burned the para aduma who spent the previous seven days in a special chamber in the Temple courtyard.
The Rambam, in Hilkhot Para Aduma (2:2), writes that this halakha was received via oral tradition dating back to the time of Moshe Rabbeinu. Apparently, the Rambam felt that the inference from the verse in Sefer Vayikra was intended merely as an asmakhta (a subtle allusion), and in truth there is no actual textual source for this law.
The implication of the Mishna is that only the soreif – the kohen assigned the role of burning the cow – was required to spend seven days in the Temple courtyard. There were several different roles involved in the procedure of preparing the purifying waters, such as slaughtering the cow, collecting the ashes, and mixing them with the water. It seems, however, that although all the kohanim involved in this process needed to be in a state of tahara, only the soreif required a special seven-day period of “protection” in the Beit Ha-mikdash. This point was made by the Tosafot Yeshanim in Masekhet Yoma (2a), where they explain that this law applies only to the kohen filling the primary role involved in the para aduma – the job of burning the cow. (See also Tosafot Ha-Rosh and Penei Yehoshua there in Masekhet Yoma.)
The Minchat Chinukh (397:17), however, takes a different view, positing that the Mishna actually refers to all the kohanim involved in the para aduma procedure. The Gemara infers from the verse that this requirement applies to “ma’aseh para” (“the activity of the para”), indicating that this includes all the kohanim involved. The Mishna speaks only of the burning of the cow, the Minchat Chinukh suggests, because this was the major stage in the process, and in any event, everything was likely done by just a single kohen. But if the roles were divided among several kohanim, then, according to the Minchat Chinukh, they were all required to spend seven days in the Beit Ha-mikdash for a week before the procedure.
Rav Yaakov Zev Yoskovitz, in his Ambuha De-Sifrei commentary to the Sifrei Zuta (Parashat Chukat), questions the Minchat Chinukh’s assumption that the para aduma procedure was normally performed by just one kohen. The Midrashic Targum Yonatan ben Uziel translation of the verses here in Parashat Chukat emphasizes at each stage that a “kahana ocharan” – “different kohen” – would perform that stage, clearly indicating that the process actually required the involvement of several different kohanim. Moreover, Rav Yoskovitz cites the Penei Yehoshua (Yoma 2a) as noting that since, as the Torah here states, those involved in the preparation of the purifying waters became tamei, a different kohen was needed for every stage of the process. Once a kohen performed one stage, he immediately became tamei and hence disqualified for the subsequent stages. It thus seems difficult to understand why the Minchat Chinukh assumed that one kohen normally performed the entire procedure of preparing the para aduma waters.