  We study the effect of hotter or colder particles on the evolution of the
chiral magnetic field in the early universe. We are interested in the
temperature dependent term in the chiral vortical effect. There are no changes
in the magnetic energy spectrum at large lengthscales but in the Kolmogorov
regime we do find a difference. Our numerical results show that the Gaussian
peak in the magnetic spectrum becomes negatively skewed. The negatively skewed
peak can be fitted with a beta distribution. Analytically one can relate the
non-Gaussianity of the distribution to the temperature dependent vorticity
term. The vorticity term is therefore responsible for the beta distribution in
the magnetic spectrum. Since the beta distribution has already been used to
model turbulent dispersion in fluids, hence it seems that the presence of
hotter or colder particles may lead to turbulence in the magnetized plasma.
