Digital Spy sat down with Shannon to discuss his research for the role, and why he doesn't necessarily view Kuklinski as cold-hearted.
Winona Ryder co-stars as Kuklinski's wife Deborah, while Ray Liotta, Chris Evans, James Franco and David Schwimmer are among the supporting cast.
Ariel Vromen directed the film from a script he co-wrote with Morgan Land.
Shannon also discussed Man of Steel, revealing that having seen the finished film, he believes that Henry Cavill was born to play Superman.
The Iceman is out in the UK this Friday (June 7).