Are Galactic Coronae Thermally Unstable?

A substantial fraction of the baryons of disk galaxies like the Milky Way is expected to reside in coronae of gas at the virial temperature. This is the only realistic reservoir of gas available to feed star formation in the disks. The way this feeding occurs depends crucially on whether galactic coronae can fragment into cool clouds via thermal instability. Here I summarize arguments suggesting that galactic coronae are not prone to thermal instability, and I briefly discuss the implications for galaxy-formation models and for the origin of the high-velocity clouds of the Milky Way.