Hearth of the Gods

The hearth in the centre of the Hall of the Gods is tended to by Hestia. It is shown to get colder and harder to keep alive when enemies approach (such as the Titans). Since, it is tended to by Hestia, goddess of Home and Hearth, it is possible that it shows that gods are welcome at Olympus. It is also possible, seeing that it is harder to keep alive, the closer enemies are, it will die if the Titans conquer Mount Olympus, in which case it shall no longer be home to the Gods. It is possible that, Hestia being The Last Olympian, the hearth would be the last to lose power, because if the Titans conquer Mount Olympus they would have to destroy all thrones.

Percy Jackson and the Olympians: The Lightning Thief
When Percy returns the Master Bolt to Zeus he sees the hearth.

The Titan's Curse
He sees the hearth in the Hall of the Gods.

The Last Olympian
Percy sees Hestia stoking the hearth.