  The temperature of the atomic matter in the Universe is held to that of the
Cosmic Background radiation until decoupling at z~100. After this it cools
faster than the radiation (\propto(1+z)^2 rather than (1+z)) and would have
fallen to about 20mK today if astrophysical feedback processes had not heated
up the interglactic medium. We show how the derivative of the Compton coupling
equation helps numerically to follow the decoupling process.
