What's the speed of that CPU? I wouldn't dare try passive cooling on any of the newer AMDs (T-bird or Duron). The problem would be concentrating the heat (even from a non-OC'd CPU) in one portion of the HS and subsquently not being able to pull that heat off effectively. I would expect that you would experience boot problems after a short time running like that.
Only thing that might do it is a good sized case fan very near or adjacent, (or even 6-8" consumer model fan) blowing across the HS...
There are supposedly a number of "quiet" fans that could be used in the popular HS/fan combos.