The special election to fill Senator Kennedy’s vacant senate seat has been set for January 19th, 2010 (a date which oddly enough was predicted right here at TMV). This would presumably mean special primaries sometime in December (one source cites December 8th), unless the parties go the convention route.
Speculation is growing the new Senator could be Joe Kennedy.
Also there is a move to change the law to allow the appointment of a temporary Senator. I’m still not entirely sure how this is legal (IE changing the law after the vacancy occurs) but I suppose it doesn’t matter if nobody stops them.