After Stanley Kubrick released his adaptation of “The Shining,” one of Stephen King’s many complaints about the film was the casting of Jack Nicholson as the family-man-cum-killer. Nicholson, King argued, was so good at conveying innate insanity that his character’s slow descent into madness wasn’t as shocking as it should be. Exploding at his wife, conversing with ghosts, chasing his son with an ax – none of this seemed like a stretch for this actor.

We can debate King’s take on “The Shining,” but his complaint occurred to me while watching Michael Shannon in “The Iceman,” even if this film is based in fact.

If it could be said that any actor was born to play Richard Kuklinski – the contract killer who murdered more than 100 men, or maybe more than 200 (he couldn’t recall), and stuck many of them in a freezer afterward, hence the nickname – it is Shannon who can switch on terrifying rage as easily as most actors can shed a perfectly timed tear.

The film opens on Shannon’s cold, chiseled stare as Kuklinski ignores a question from a prison warden – “Do you have any regrets for the things you’ve done?” – and the face tells us everything we need to know about the man. After hitting the roof to varying degrees in films such as “Take Shelter,” “Revolutionary Road” and “My Son My Son What Have Ye Done,” Shannon makes Kuklinski’s cold-blooded killings seem like second nature.

But Ariel Vromen’s biopic is concerned with Kuklinski as a family man as well as a mass murderer – a fair-minded perspective that’s as unadmirable and unoriginal as it sounds. We learn of Kuklinski’s dual nature early on, as he hesitantly charms his soon-to-be-wife Deborah (Winona Ryder) and tells her he works in cartoons, even though he’s really bootlegging porn for the mafia.

His work gets him embroiled with New York City kingpin Roy DeMeo (Ray Liotta), who threatens him with a gun when he messes up a delivery. Kuklinski is unperturbed. DeMeo, impressed, later takes Kuklinski out for a drive and asks him to shoot a homeless man on the street. Kuklinski does it. Less than 25 minutes into the movie, we’re treated to a montage of Kuklinski casually strangling, shooting and stabbing men who are anonymous to us and him. Killing is his calling, and business is good.

Meanwhile, Kuklinski returns to his suburban home in New Jersey every night to banter with Deborah and prepare for his daughter’s birthday parties. He tells them he works on Wall Street. They don’t ask any questions.

Taking the “Iceman” moniker literally, Bobby Bukowski’s cinematography renders Kuklinski’s work and family life equally cold – the exteriors are saturated in blues and grays, the rooms feel colorless. And Shannon, as usual, makes his outbursts even scarier by keeping them buried under a calm and collected visage. But as decades pass, and as Shannon picks up a goatee and sideburns along the way, the narrative tries to color Kuklinski with the conflicts of a man wanting to do well where it matters.

He meets a like-minded murderer, Mr. Freezy (Chris Evans) – the two chit-chat while carving corpses in a freezer – and swears to him that he’ll never kill women or children. He visits his brother (Stephen Dorff) in prison and castigates him for murdering a child. A brief flashback hints at an abusive childhood. It all just melts your heart, doesn’t it? By the film’s end, this anti-hero is all but treated like a hero, as he tries to fend off the mafia when it closes in on his family.

It is compelling and unnerving when a film forces us to realize the humanity of terrible humans – “Monster” did so for Aileen Wuornos, just as “Downfall” did for Hitler. But “The Iceman” goes further by asking us to lend our most conventional sympathies to Kuklinski. The film sees something complementary, rather than contradictory, in his roles as a stone-faced serial killer and struggling family man. It’s an approach that’s either credible, quixotic or offensive – depending on how Iceman-esque you are in stretching your morals.