... on the temple of Vesta. Vesta was the Roman goddess of hearth and home. Her temples were, as far as I can recall, always round. A plaque (probably modern since it's written in Italian, not Latin) indicating the reason for that can be found on the side of the base. I hope you appreciate that I had to translate some verbs from the dreaded subjunctive form here:

"Aedes Vestae
Sembra che Numa Pompilio, re dei Romani, abbia costruito il tempio di Vesta rotondo, avendo creduto che della stessa forma fosse la terra, da cui dipende la vita degli uomini."

I'm sure I'll be told if I have this wrong but to me this reads:
"It seems that Numa Pompilio, King of the Romans (specifically the second king after Romulus) has constructed the temple of Vesta (in a) round (shape), having believed that it is the same form as the Earth, on (literally "from") which depends the life of mankind (literally, "the men")."

These ruins look a little better than some, and there's a reason for that; from what I can tell they are in fact not truly restored but rather reconstructed in the 1930s.

Yes, the 1930s. Yes, that means Mussolini. I've found one or two references to Mussolini having been behind this reconstruction (including Wikipedia, which obviously I don't trust) but nothing definitive. I have no reason NOT to believe it was the case. It is entirely possible though that history is loath to credit Mussolini with anything positive. If this is so, I do not like it. History should be what it was, not "spun". Even if he was responsible for this reconstruction (and for the construction of the first subway in Rome which, as one tour guide said, could only have been done by a dictator), that takes nothing from the unconscionable price that far too many people paid for his achievements. History needs no "spin", but I know that it gets it anyway. (Speaking of which, no, the ancients did NOT universally believe that the Earth was flat. Some of them DID notice the curvature of the horizon and the fact that ship masts appeared before the hull and drew the correct conclusions. That makes the plaque above quite plausible.)

But getting back to actual history, the temple housed the sacred flame which was tended by the priestesses of the order; the Vestal Virgins. I thought I'd try to kick in a little solar flare as a hat tip to that flame.