Most of the Olympian gods and goddesses had temples, but the goddess Hestia
(Roman Vesta) was different. In Rose Williams' new book Gods and Other Odd Creatures
, she says that the Greek goddess had as her sanctuary the prytaneum
that was located in the center of the city, just as the hearth was the center of the home. Both places held a fire. Colonists set out with a coal from this city fire to start a new civic fire upon arrival at the new location.
In Rome, Vesta had a shrine or aedes, but not a templum. The reason it wasn't a temple is that it was already holy by virtue of the sacred fire, and so needed no consecration by the augurs. The sacred fire of the Aedes Vestae, which was tended by the Vestal Virgins, burned until A.D. 394.
See Gods and Other Odd Creatures, by Rose Williams.