Fred would be wise to go with a strong debater with proven exective experience and a dynamic personality that would balance his low key personality. That person would be Mitt Romney.That just wouldn't happen. Mitt is Fred's main target right now, as he needs the same conservative voters that Mitt is courting in order to overtake Rudy. Fred will be contrasting his lifelong Movement conservatism with Mitt's very recent conversion. And likewise, Mitt, already a bit of a dirty campaigner, will be defending his turf ferociously. The inevitable tension and animosity I think will create a situation making it impossible for Fred to pick Mitt. Plus there is the fact that Mitt doesn't bring anything new to the ticket.
If I where Thompson I would be afraid of being stabbed in the back by Rudy. Rudy has too much political ambition. I believe as VP he would constantly be jockeying for position for 2012 and not focused on implementing the policies of the President.