  We give an exact information-theory treatment of the $n$-dimensional
black-body radiation process in a non-extensive scenario. We develop a $q$
generalization of the laws of i) Stefan Boltzmann, ii) Planck, and iii) Wien,
and show that conventional, canonical results are obtained at temperatures
above $1 K$. Classical relationships between radiation, pressure, and internal
energy are recovered (independently of the $q$-value). Analyzing the particles'
density for $q\approx 1$ we see that the non-extensive parameter $q$ introduces
a fictitious chemical potential. We apply our results to experimental data on
the cosmic microwave background and reproduce it with acceptable accuracy for
different temperatures (each one associated to a particular $q$ value
