I came upon an older, but very interesting article on Ancients Origins today, about ever burning lamps, which were used in many of the temples of the Theoi--they were lamps that were kept burning throughout the year, and usually only refilled once a year (such is the tale, anyway) in an elaborate ceremony.

As the article mentions, ever burning lamps have been recorded by writers from various parts of the world at different points of time. In the ancient world, for instance, the writer Plutarch mentions in his work ‘De Defectu Oraculorum’ that a lamp that burned over the door of the temple of Jupiter [Zeus] Ammon in Egypt. According to Plutarch, the priests of the temple claimed that the lamp stood in the open air, and neither wind nor rain put it out.  Similar accounts are given for the altar of the Temple of Apollo Carneus, at Cyrene. Pausanias wrote about a gold lamp in the temple of Minerva [Athena] Polias in Athens. This lamp, which was built by the scholar Callimachus, was said to have been able to maintain a flame steadily for a year without needing refuelling or having its wick trimmed.

We have very, very little knowledge about these lamps and the practices around them, but we know that fire was very important in ancient Hellas. Back in ancient Hellas, most religious activities surrounding the household revolved around the central hearth, which was seen as the physical manifestation of Hestia. All the household fires were lit with a flame from the prytaneion (Πρυτανεῖον), the structure where state officials met and where the city kept a fire for Hestia burning day and night. Every single heart fire in the city or town was linked to that central one. This network of fires, which were never allowed to go out, brought all Hellenes together. It would not be odd to think that temples took part in that practice as well.
There is still a lot to discover about ever burning lamps, their purpose, and how they functioned, but for now, we can imagine how beautiful their presence would have been in a large, dark temple--a focal point of worship that would always have been there. Hopefully in years to come new archaeological proof will be found to explain this practice, and scholars will pay more attention to it. For us Hellenists, dreaming of building temples, an eternal flame would be a beautiful addition to them.