We present empirical evidence for a radiative cooling time for the Io plasma torus that is about a factor of ten less than presently accepted values. We show that brightness fluctuations of the torus in the extreme ultraviolet (EUV) at one ansa are uncorrelated with the brightness at the other ansa displaced in time by five hours, either later or earlier. Because the time for a volume of plasma to move from one ansa to the other is only five hours, the cooling time must be less than this transport time in order to wipe out memory of the temperatures between ansae. Most (~80-85%) of the EUV emission comes from a narrow (presumably ribbon-like) feature within the torus. The short cooling time we observe is compatible with theoretical estimates if the electron density in the ribbon is ~104/cm3. The cooling time for the rest of the torus (which radiates the remaining 15--20% of the power) is presumably consistent with the previously derived 20-hour values. A nearly-continuous heating in both longitude and time is needed to maintain the EUV visibility of the torus ribbon-a requirement not satisfied by presently available theories.¿ 1997 American Geophysical Union