Joseph Gordon-Levitt and Shailene Woodley Get to the Bottom of a Murder in “Killer Heat” Trailer (Exclusive)

'Killer Heat,' based on author Jo Nesbø's 'The Jealousy Man,' is on Prime Video Sept. 26

Joseph Gordon-Levitt and Shailene Woodley team up for a murder investigation set in Greece.

PEOPLE has the exclusive first trailer for Amazon MGM Studios' Killer Heat starring Gordon-Levitt, 43, as private detective Nick Bali working on the Greek island Crete. He is hired to investigate the accidental death of a young man from a rich family on the island.

Richard Madden plays both victim Leo Vardakis and his identical twin Elias, while Woodley, 32, is Elias' wife, who suspects someone in the Vardakis family conspired to murder one of the twins.

As detective Bali embarks on the investigation, he finds the wealthy family controls much of what happens on the island and reckons with his own difficult past and estranged family.

"There's a part of me, as I think there's a part of so many of us, that just loves reading a good mystery," Gordon-Levitt tells PEOPLE of the movie and the short story it is based on, Jo Nesbø's The Jealousy Man.

He, Woodley and Madden, 38, filmed much of the movie on location in Crete, and Gordon-Levitt recalls that filming the movie satisfied a lifelong urge to travel for his work.

Related: One Last Thing with Joseph Gordon-Levitt: How Fatherhood Turned Him Into a ‘Big Softie’ (Exclusive)

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"I just consider it such a privilege. I feel so lucky," he says. "I've gotten to go to lots of different places and there are very, very few places I've been that were more beautiful than the island of Crete. I've never been to Greece before getting to do this movie, and it's a cliché — the beauty of Greece — but it's a cliché for a reason. It's flipping beautiful!"

The movie marks a reunion for Gordon-Levitt and Woodley, who last costarred in 2016's Snowden. Gordon-Levitt says he and Woodley had not spoken in a few years but they lept "right back into all the comfort and friendship that you've had in the past."

"That's how you know it's a real good friend, and that's just like it was with Shae," he adds. "I was like, 'Hey, want to go to Greece?' I'm so happy it worked out."

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"I think if you're like me and you are enticed by some juicy characters, gorgeous settings, Shea and Richard both are so good in the setting of island of Crete, you really couldn't ask for a more beautiful place in a world," Gordon-Levitt says. "If you want to just let a vibe wash over you, I think you'll enjoy this movie."

Killer Heat is streaming globally on Prime Video Sept. 26.

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