In the movie, McQueen plays a bounty hunter, and while in "Bullitt" he's quite the wheelman, that's not the case in this one. McQueen's character, "Papa" Thorson, is a horrible driver, and the Trans Am is far too much car for him. A chase sequence sees McQueen driving a combine harvester to catch the perps who are driving his stolen rental Pontiac, and the Trans Am ends up blown in half with dynamite, then returned to the airport on a trailer.
The driver of said GMC truck and trailer combination, Harold McQueen (no relation), received the title of the first car used in filming, and for the following decades planned to fix the now-ruined car, but never got around to it. Instead, the 1,300-mile Pontiac wreck sat on a farm for nearly 40 years, until Harold decided to sell it to an enthusiast. There's studio documentation proving the car's pedigree, and stunt modifications can be seen in the Pontiac's floor and dash. While it's obviously in dreadful condition, the car remained more intact than the other stunt car the film crew blew up even more spectacularly — that car ended up as the pile of parts in the airport scene, and those bits and pieces were eventually dropped off at a junkyard after a Pontiac dealer refused them.
McQueen did also drive a 1951 Chevrolet in the film, and kept that yellow convertible after filming was wrapped up. Sadly, he was diagnosed with cancer just a month later, after reportedly being in poor health during the shooting, and passed away in December 1980. The yellow Chevy stayed with his estate for some years, later getting restored and auctioned.
Right now, it's not clear what the Trans Am's fate will be. The car's current owner, Calvin Riggs from Carlyle Motors in Katy, Texas, wants to know more about the Trans Am and the film shoot: His post on Hemmings includes a lot of information, but more would be useful.