One of the main themes is that of competition and "keeping up with the Joneses" mentality of the women in the story. From the very beginning, Mrs. Slade and Mrs. Ansley are competing for the same man--Mr. Slade. One ends up marrying him, and considers herself the "winner," but can't understand why she is still envious and jealous of her "friend" who married another man. It is only in this story set in Rome,where the two are talking and Mrs. Ansley is knitting calmly, that it is revealed that Barbara Ansley, the dramatic and vivacious one (of whom Mrs. Slade is envious since her own daughter is quiet and not so amazing) is the daughter of Mrs. Ansley and Mr. Slade.
The story gets it's name from a fever caught in Rome if one stays out too late in the night air. Mrs. Slade, in her youth, wrote a note to entice Mrs. Ansley out into the air in hopes that she would contract the fever and be out of the running for Mr. Slade. However, the note was supposedly written by Mr. Slade, and unbeknownst to Mrs. Slade, her friend answered the note. So, the fake meeting actually happened. The two had a rendezvous, and Barbara Ansley was conceived. Mrs. Ansley was hurried into a marriage to cover her problem, and the two women have lived in close proximity to one another in the same social circles ever since.
The theme of competition then, is trumped when Mrs. Slade realizes that she didn't really win anything...the vivacious daughter is her husband's by another woman, and Mrs. Ansley seems very happy in contract to Mrs. Slade's misery.
To see the subtle nuances Wharton includes in the story, go back and read it again focusing on the tone of the women's voices, their body language, the silences between them. They have been forced by circumstances beyond their control since youth to spend time together, yet they don't like one another much at all.