Like his character in the new spy thriller “The Coldest Game,” Bill Pullman has suddenly found himself uprooted from his daily life in the U.S. and dropped into an elaborate setup in Warsaw, Poland. In what he estimates is the shortest prep time he’s ever had for a feature role, Pullman agreed at the last minute to replace an injured William Hurt as a hapless, obsessive, burned-out American chess master who becomes a pawn in a 1960s Cold War plot.

“This was kind of scary to me,” Pullman tells Variety, “and therefore, I thought, worth a try.”

Pullman was brought in to play Joshua Mansky just a few weeks into filming, managing to squeeze in the Warsaw shoot between the first two seasons of his current USA Network project, “The Sinner,” after Hurt broke his leg in an off-set accident. Set to wrap a 40-day shoot next month, the thriller is written and directed by Lukasz Kosmicki, and produced by Piotr Wozniak-Starak and Krzysztof Terej of Watchout Studio, plus producer Daniel Baur of Germany’s K5.

In the film, Pullman’s character, despite limited social skills and some substance-abuse issues, is recruited by a seductive CIA agent (played by Lotte Verbeek) and abruptly flown to Warsaw to face off against a Russian chess champ (Evgenij Sydikhin) at an international tournament in the iconic Palace of Culture and Science, a genuine Cold War relic that in real life still dominates the city center of the Polish capital. The match turns out to be a sort of proxy for the Cuban missile crisis in Kosmicki’s film, one of the first Polish productions to be shot in English.

Hurt’s unexpected departure was just one of the challenges facing “The Coldest Game.” Aptly enough, given the film’s title, the weather was another. While filming one night earlier this month on the roof of the culture palace – an imposing structure erected in 1955 in homage to the Seven Sisters building in Moscow, once the pride of Stalin – Pullman wore just a blazer, dress pants and loafers even as ice and snow surrounded the crew amid record low temperatures.

“It was minus-14, but it was blowing,” Pullman said during a break in shooting on a U.S. embassy set designed by Oscar-winner Allan Starski (“Schindler’s List”). The nearly perfect mockup of the 1960s-era diplomatic outpost, built by the crew in an empty building that once served as Gestapo headquarters in Poland, is full of period furnishings and 50-year-old back issues of Life lying about.

In one scene featuring a phone call from President John F. Kennedy, Pullman’s Mansky finds himself reluctantly saddled with intelligence duties as he preps for the next chess match, bristling: “I knew it’s not about the chess.”

Pullman said his fascination with the character grew as he quickly read through Kosmicki’s script. Mansky, a complex man who resents authority and lives mainly inside his head, is unlike any other character he has taken on, the affable actor said.

“He’s a little bit of a wild card,” Pullman told Variety. “And I had never played chess before.”

Determined to make the character authentic, director Kosmicki hired a chess master to help him write critical game scenes with actual moves from historic matches, including one in which Soviet players tried to distract an opponent with a hypnotist. Pullman himself boned up on chess, meeting Polish grandmaster Monika Socko and studying the moves of players currently competing in Warsaw.

The matches in the film are each shot in a distinct visual style. Cinematographer Pawel Edelman (“The Pianist”) has been working closely with the Kosmicki to create a look that evokes classic retro thrillers, with a single camera in most scenes, and occasionally intricate choreography with actors on elaborate tracking shots.

The project is an ambitious one but is being produced by a relative upstart: Watchout Studio is only a few years old. However, it has had major commercial success domestically in Poland with its Polish-language projects. Producer Terej said that the international cast and appeal of the story made it the company’s greatest challenge yet. The project has backing from the Polish Film Institute and a sales deal with L.A. shingle Hyde Park Entertainment. It’s aiming for release next year.

The film’s thorough prep, which included blocking each scene well in advance on special software, has helped keep the film crew on their toes, Kosmicki said, with morale high even when shooting on real Warsaw streets from which they’ve had to remove masses of snow.

“They know that we know what we want to shoot,” Kosmicki said.

(Pictured: Lukasz Kosmicki and Bill Pullman)