Mr. Criss, 30, leaned over and pointed out the window. “See that?” he said. “That’s the houseboat, perfectly recreated.” In Indian Creek, the crew had built a replica of Mr. Cunanan’s final hide-out, where he met his demise after a frenzied eight-day manhunt. The series makes use of several real locations in Miami Beach, most notably the Versace Mansion, the site of the murder, now a boutique hotel.

As the car turned into a parking lot full of trailers, Mr. Criss was all smiles, doling out greetings of “Hey, man!” and “Happy last day!” Even pre-caffeine, he was relentlessly chipper, which seems antithetical to playing a murderer. Or maybe not. Charm was Mr. Cunanan’s calling card, masking a desperate need for acceptance that curdled into pathology. And Mr. Criss’s exuberance on set, he said later, was a way of putting the crew at ease.

“This is the first time I’ve been No. 1 on the call sheet, so you’re kind of the quarterback,” he said. “You set a tone. I take my work very seriously, but I don’t take myself seriously at all.”

He plopped down in front of a mirror, where a hair-and-makeup artist fitted him with a wig. Like any decent actor playing a villain, he had looked for Mr. Cunanan’s redeeming traits: his talent, his likability. “The bleeding idealist in me always likes to think that there are more things in common between all of us than there aren’t,” he said. Presumably, he meant “bleeding-heart idealist,” but the phrase seemed apt.