There are various techniques for building tension in a story: the use of foreboding, the ominous comments of hindsight, the race against time or the ticking clock set-up, the sudden reversal of fortune or the shock revelation that trips up the reader and changes what we understand of the narrative. Writing in the present tense can also contribute to the breathless, fast-paced feel of a thriller. With this technique there is neither foresight nor hindsight. We do not have the bigger picture, only the frame by frame, chapter by chapter account. Like the protagonist we are in the moment. It’s a very modern style, well, I assume it is (people who know about the history of literature please correct me if I’m wrong).
I’ve written novels in the present tense and others in the past. Sometimes I’ve found that changing to the present tense gives a better edge to a story. In my latest book, Blink of an Eye, one character’s narrative is written in the present and the other is in the past though it covers the same time-frame. As with most choices your first instinct is usually the correct one but if you’re unhappy with the flavour of the prose then tense is one element to consider. Write a chapter both ways and compare. Like POV the tense should suit the story and work for the characters.