Does the former Wisconsin governor and Secretary of Health and Human Services stand a chance?
Thompson has always struck me as a straight-shooter. His time at HHS was marked by some alienation from the Bush White House, which may be an asset in GOP circles in 2008. (His was one of the early gubernatorial endorsements for Texas's governor, George W. Bush, the collection of which proved to be the foundation of his successful drive to the Republican nomination in 2000.) There are questions about Thompson's handling of his past major political offices.
The fact is, the 2008 Republican nomination is wide-open. (Or as wide-open as the Republican presidential nominating process gets.) Enthusiasm for McCain is flagging. Because of his liberal views, Giuliani is unlikely to win the nomination. Romney has a shot, but I think that he's so afraid of replicating his father's experience in 1968, that he's a robotic campaigner.
The informal rules of "succession" are different in Republican circles. Republican voters tend to play it a bit safer than do Democratic ones, sticking with known entities, making it tougher for dark horses to win their party's nomination. That's a definite mark against Thompson. McCain is the clear successor for the Republican nod.
But, being a governor is always a plus in a run for the presidency. By most accounts, Thompson had a good tenure as in Wisconsin.
If he can catch fire in Iowa, he could make it interesting.
(See here, here, and here.)