He added: “It’s a place where you can’t take your phone, and there are no recording devices. People are disrobed. People are exposed to a degree that they never are in public, and so it’s a place for really honest negotiations. I think of it as a very even playing field.”

He also began thinking of it as a place where he would love to see a play staged, though it was more a fantasy than a plan. But after he saw a 2007 revival of “Dutchman” at the Cherry Lane Theater in Greenwich Village — the theater where the play had its premiere, and won an Obie — he became more serious about the idea. And when RoseLee Goldberg, the founder of Performa, approached him about participating in the biennial, bringing the play and bathhouse together started to seem possible.

The setting of the play itself is a subway car, in which the woman, a seductress named Lula, and the man, Clay, a budding young intellectual, meet seemingly by chance and have a conversation that veers quickly from tension and eroticism into the open wounds of civil-rights-era racial politics. Mr. Baraka’s set descriptions depict a 1960s pre-air-conditioning subway — “in the flying underbelly of the city steaming hot” — but they could easily pass for the baths, an ambiguously public place where strangers also come to sit next to one another for a while for a common purpose.

The new setting, Mr. Johnson said, seemed not only fitting but also necessary for exploring his interest in the play, which some critics dismiss as a relic of its time and of Mr. Baraka’s Black Nationalism. “People have this expectation that theater and art are inherently generous,” Mr. Johnson said, “that they’re there to cater to them rather than to produce problems. And I was interested in this because I want to see something that pushes people up against their limits. The heat is an enormous factor in that. The level of comfort and discomfort is very important to me.”