Matter temperature after cosmological recombination

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.