Temples would not have kept relics. Corpse pollution was one of the major forms of ritual impurity in the Greek world--even the healing temples dedicated to Asclepius, where sick people went for healing, didn't allow certain sick people in, on the chance that if they died they would pollute the temple. Keeping a piece of a dead body there would have been unthinkable, as far as anything I've encountered. Miasma by Robert Parker is a very thorough discussion of ritual purity and pollution in general, and has a lot of discussion of death.

There were cultic practices around tombs, both within families and on larger, civic scales. Civic cult to heroes and deceased rulers would either center around the tomb and not within a standard temple, or would be in a temple and not a tomb. Celsus was buried in the library in Ephesus, but that was comparatively late (during Hadrian's reign). And it was noteworthy that someone should be buried within city limits, let alone in a major building.

So the issue isn't really whether divine honors and/or apotheosis had any connection to the physical body (that question doesn't have the same answer across time and space in the ancient Mediterranean), but the fact that having parts of human corpses within places of worship was fundamentally disgusting to Greeks and Romans.