The first Mishna in the (perek (68b) teaches that the kohen gadol read the Torah publicly before the people who came to the Temple to see the avodat (Temple service of) Yom Kippur. It further itemizes the eight blessings that the High Priest recited over this reading. They include a blessing on:
Modim (a blessing of thanksgiving)
a request for forgiveness
the Temple itself
the kohanim (that their sacrifices should be accepted)
the Jewish People
the rest of the prayer.
The Sages taught in another baraita: And the blessing concerning the rest of the prayer reads: Song, supplication, petition before You for Your people Israel, who need to be saved. And he adds an additional supplication and concludes the blessing with: The One Who hears prayer [Shomei’a tefilla].
Although these are the blessings enumerated in the Mishna, there are a wide variety of opinions about the actual blessings recited and their number. For example, the Meiri suggests that there really were ten blessings recited, since the normal blessings made before and after Torah reading should not be counted, since they are not unique to the avoda of Yom Kippur. He adds a blessing about the city of Jerusalem.
Most of the blessings that are unique to the Temple service no longer appear in our liturgy. Nevertheless there are some exceptions. For example, Rashi says that the blessing on the avoda is similar to the retzei blessing that is said in the daily amida, with a different closing blessing. Rather than using the contemporary prayer for the return of God’s presence to the Temple (which would obviously have been inappropriate when the Temple was standing and in use) the blessing concluded she-otkhah levadkhah be-yirah na’avod – that only You should we serve in awe. According to some traditions, this blessing is retained on the occasions when the kohanim bless the congregation on holidays during the musaf prayers.
Some suggest that the blessing recited over the Temple was to the effect of “It should be Your will that You should establish Your Temple forever, and be desirous of it and allow Your holy presence to reside in it forever, blessed be You God, who dwells in the Temple.”