Frist is running, no doubt about it. The Bush machine knifed Trent Lott so Frist could become Majority Leader and get some national publicity. Now Frist isn't running for a third term as Tennessee Senator.
That's because Tennessee's Governor is a Democrat. If Frist runs again, then Phil Bredesen will nominate a Democrat for his seat should Frist win the Presidency. So another Republican must keep that seat.
Job one for Tennessee Democrats - find a candidate who can win that Senate seat.