There is a huge difference between writing a thriller book as opposed to that of a screenplay for a thriller movie. However, the elements of the story are pretty much the same. Screen plays talk about acts 1, 2 and 3, while a book should be about a beginning, middle and end.
I recently came across this article produced by the Tennessee Screenwriters Association, where they lay down a 'loose formula' for writing thriller screenplays. I think it's a great resource for thriller writers in any medium. Why not take a look?
The only point I don't quite agree to is this:
'The Thriller hero most often lacks the physical skills of an Action/Adventure hero - while the hero may ultimately perform a physical act to reach safety, the principal energy of the story is devoted to ingenuity, the hero solving a puzzle to expose the corruption of the villain and extract him/herself from danger."
My reason for saying so, being, the hero can have the physical skills (ala Joe Hunter) but have an outside weakness i.e. his brother has been taken by a serial killer, he has to protect a woman from a contract killer hell-bent on killing her, he has to protect some innocent children from a group of extremists etc. I think a thriller can have a tough guy hero, but it is the extreme danger of the situation he is in (as in all the other points) that define the thriller. But I'll leave you to draw your own conclusions.