Byzantine Christians performed no animal slaughter and scoffed at the notion of a rebuilt Jerusalem temple (its destruction was a sign of Christ’s divine mission, according to most), but I wonder if they did not treat their more sacred edifices with the same reverence as the Jewish temple and appeal to similar symbolism in their conceptualization. The Church of the Holy Sepulchre seems to me to be the most clear example of this practice.
I was reading a portion of Eusebius’ Vita Constantini and something jumped out at me. At one point he calls the cave over which the superstructure was built the “holy of holies” (3.28: αγιον των αγιων). Shortly thereafter he explains that the cave opens to the east, sitting at the west end of the building which also opens to the east. The orientation seems to appeal to that of the Jerusalem temple (eastward orientation is consistent in a number of ancient Near Eastern temples). A 4th century floor plan is found here. The imagery represented here is clearly that of a temple structure, but I believe the relationship goes deeper than architecture.
Ultimately the purpose of an ancient temple was to delineate and protect sacred space, and numerous times throughout Eusebius’ text he refers to the cave as holy. The cave acts as a natural delineation of space, but the edifice surrounding it is clearly intended to protect as well as showcase the most sacred space under its roof. Sanctification and communion with God were the immediate goals of temple visitors, and the Church of the Holy Sepulchre, throughout history, has been treated as just such a location. Elsewhere Eusebius explicitly calls the structure a “temple” (3.40: των νεων). At 3.33 he explains that Constantine built the New Jerusalem over the old, as spoken of by the prophets. The Church was to represent the “chiefpart of the whole work.”
Christianity rejected the necessity of a temple of God, often arguing quite vitriolically against it, but it seems something of the luxury, palpability, and cultic significance of the defeated Jerusalem’s temple was lacking in early Christianity. While the physical temple was seen by Byzantine Christians as a base relic of tribal religion, there seems to have survived a need for holy space, where the presence of God’s spirit could reside for those who sought it. This may have been accomplished to some degree through the edification of the Church of the Holy Sepulchre, although any relationship with the temple ideology of Judaism was ignored.