  The classical Friedmann-Lema\^itre equations are solved using a corrected
version of Planck's radiation law. The function curves of the scale parameter
a(t) and the variations with temperature a(T) and t(T) are given. It is shown
that a reasonable cosmological evolution is only possible in case of flat
spatial slices (k=0). The initial singularity is avoided. Horizon and flatness
problems do not exist. For low temperatures compared with the Planck
Temperatur, the equations yield the usual course of expansion of the standard
FLRW model for a radiation universe with k=0 and p=u(T)/3.
