The double meaning of "Roman Fever" is that it refers literally to an feverish ailment to which one is susceptible in the cool air after sunset, and figuratively to a feverish battle for Delphin Slade by two women who were rivals for his love.
On their second trip to Rome, one in which they are the spectators rather than the actors in what occurs, Grace Ansley and Alida Slade sit quietly on the parapet watching the sun set over the ancient city. They are
...two ladies who had been intimate since childhood [but they] reflected how little they knew each other.
Both ladies have "visualized each other...through the wrong end of her little telescope." Mrs. Slade thinks of how Mrs. Ansley is much less articulate than she; Mrs. Ansley thinks about how "Alida Slade's awfully brilliant, but not as brilliant as she thinks." Clearly, they yet harbor feelings of rivalry between them. For a while they sit without speaking. In fact, they have met by coincidence as they are staying at different hotels, having been unaware of the other's plans to visit Rome. This situation is ironic because so many years ago neither was aware of the other's schemes then, either. For, Grace Ansley had no idea that the note to meet Delphin at the Coliseum was forged by Alida, nor did Alida know that Grace replied to Delphin and he actually met her that night. In fact, she conceived her daughter Barbara that Roman evening, and was later confined at home not because she was sick, as people had thought.
These revelations between the two rivals who were once thought of by others as friends, change the scope of their relationship forever. While their return to Rome has given no one an ailment because of the cool evening air, there has certainly been a fever of emotional honesty.