Trask plans to capture the mutant Mystique (played by Jennifer Lawrence) and use her DNA in android sentinels who will hunt and kill other mutants and anyone else who gets in their way.
To stop him, Wolverine (Hugh Jackman) must go back in time and work with the young Charles Xavier (James McAvoy) and Magneto (Michael Fassbender) to prevent a war that is happening in the future.
He is quite obviously the film's villain, but Dinklage denies his well-coiffed, bushy moustached character is off his rocker.
"Mad? He's just trying to save humanity," he laughs. "He can't let it screw up his coiffed hair. That's all me, by the way - it's all my hair with a lot of blow-dryer and product."
In recent years, Dinklage has worn a costume of a different kind. As the quick-witted, hard done-by Tyrion in Game of Thrones, he is widely regarded as the backbone of the fantasy drama, winning an Emmy and Golden Globe Award for his work.
But by occasionally playing the bad guy, he hopes to avoid getting stuck in that - or any other - role. He says the key is to mix it up, not to repeat what's been done before and avoid being comfortable.
"I know that sounds funny, but I like to be challenged and I don't like repeating myself. I am about to go do a crazy Adam Sandler comedy right now, like, why not? I don't want to go and do Game of Thrones on my time off from Game of Thrones. I want to play a businessman; I want to go have fun with Adam Sandler."
Dinklage, 44, was born with achondroplasia, a common form of dwarfism. And while his physicality has played a huge part in forming his Game of Thrones character, he says almost the opposite is true in X-Men: Days of Future Past.
"What I really liked about this film is that there's really not much to do with my size. And maybe you could see it as a form of mutation, but [Trask] gets the short end of the stick - he's short but he can't walk through walls, claws don't come out of his hands and he doesn't have the power to control metal. He just has this intelligence.
"[Director] Bryan Singer and I talked about that; that there's an element there, that sort of self-loathing, jealousy thing and that's interesting to play."
Embodying a character on a path to wipe out anyone who is different was an interesting personal challenge for the New Jersey-born actor. He says when he was younger, he spent a lot of time - maybe too much, he thinks - trying to reassure people, to make them "okay" with who he was. But over the years he decided that wasn't his job any more. "I was like, 'I'm done with that. Think whatever you want to think of me. I am tired of doing that'."
And while he was never aware of people being afraid of him because he was different, he says he had to work hard to make people take him seriously.
"Of course we fear the unknown, and we exploit it constantly in our society throughout human history, protecting our own.
"And we have always used that. And this guy Trask, he definitely exploits people's fears and profits from that, and there's always somebody profiting from fear, that's the scary part of it all. I mean, war profiteers, big business, they have got to exploit people's fears and profit from it. That's the reasoning behind it, and that's what this guy does."
As far as dissecting the pros and cons of special mutant powers, Dinklage says he's afraid of what he would do if he couldn't be seen, but he would quite like the ability to change his appearance.
"I wouldn't trust myself with invisibility, I really wouldn't. That would be such a dangerous powerful thing. Don't let that be an option for me, because that would be so great and horrible.
"We won't get into the naughty reasons, will we?" he says laughing. "But Mystique is pretty cool. People will read that and think, 'oh Peter Dinklage likes to dress up in women's clothing and paint himself blue'.
"But she aspires to what we do as actors - live briefly in other people's lives and do it convincingly. She's the Daniel Day Lewis of mutants basically, with that transformative skill that he has. And I like the colour blue and wearing women's clothing."
Who: Peter Dinklage
What: X-Men: Days of Future Past
When: Opens in cinemas today
- TimeOut
