Roman Fever sounds like something we'd like to have. Turns out, though, it's just malaria. Yep, the mosquito-borne illness. Not as awesome as we'd hoped.
Back in the day, people thought you'd contract the disease from being out at night in secluded areas. So basically, you get "Roman fever" in the same way you get a reputation for being fast and loose. And that's no coincidence. Check out the scene when Winterbourne catches Daisy and Giovanelli in their late-night tryst at the Colosseum and warns her she'll catch Roman fever (remember now, that's both malaria and a bad rep):
"I don't care," said Daisy, in a strange little tone, "whether I have Roman fever or not!" (2.257)
Hmmm. Her strange little tone implies that she does care, maybe just a little, as it could cost her her true love—Winterbourne—and, far more importantly, her life. Being out in the buggy Roman night with a strange, touchy Roman stands to rob Daisy of her health and her squeaky-clean image.
The name "Roman fever" is also ripe for punning, which Henry James just loves. Edith Wharton, James's good friend and mentee, used it for the title of a 1934 short story about adultery. It can mean anything from the attraction American women experience towards Roman men to the romantic appeal of the ancient city itself.
"Fevers" in general connoted having gone a little crazy, as they still do today—like Spring Fever, Cabin Fever, Bieber Fever—you name it. What exactly is Daisy crazy for? Lust, attention, excitement, or foreignness? All of the above. Check please.