The governor of Wyoming is a Democrat and, usually, that would mean that Senator Thomas' successor would be a Democrat. However, the linked story has this to say about the process of filling a Senate vacancy in Wyoming:
Gov. Dave Freudenthal, a Democrat, will appoint a successor from one of three finalists chosen by the state Republican party....I've never heard that before.
According to Peggy Nighswonger, Wyoming's elections director, the governor has five days to appoint one of the party's three nominees once he receives the names. That person will serve until the next general election in 2008.