Thompson's background suggests he will grow the size and scope of the federal government. I don't trust him to become a conservative now just because he's telling people he is.
I understand folks have some issues with Thompson's past, but growing the size and scope of the government is not one that is grounded in reality. The only case that could be made for that is McCain-Feingold, which at least is within the scope of the federal government regulating federal elections (even if some of the provision were bad ideas).
As for the rest, see my tagline -- this is the same approach he took in the Senate as today.