On the set of the third season of “The White Lotus,” which shot for seven sticky months in luxury hotels in Bangkok and Koh Samui, Thailand, the writer and director Mike White had a repeated note for the actor Patrick Schwarzenegger.

“You’re not walking rich enough,” White would yell across the pool deck. “Patrick, be richer.”

Schwarzenegger, 31, recounted this — incorporating an impeccable White impression — on a bright morning at a coffee shop in the TriBeCa neighborhood of Manhattan. (Schwarzenegger described himself as a coffee “addict.” His on-set nickname: Cold Brew.) In person, he was polite, earnest.

“I’m thankful each and every day for the life that I’ve been given,” he said as he spooned up yogurt and berries.

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In the current season of “The White Lotus,” Patrick Schwarzenegger plays the oldest child in a privileged North Carolina family. Sam Nivola and Sarah Catherine Hook portray his siblings.Credit…Fabio Lovino/HBO

White saw this guilelessness as genuine. “Patrick is just somebody who likes people, and people like him,” White said on a call earlier that week. “He’s a sincere actor, but he’s uncomplicated in his presentation of self.”

Schwarzenegger had come into the city to do a few days of press for “The White Lotus,” his most high-profile project to date. He plays Saxon, the eldest son of a wealthy North Carolina couple (Parker Posey and Jason Isaacs). A cocky finance bro, Saxon’s preferred pastimes include smoothies, pornography and observations about his siblings’ sex lives.

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