  Intergalactic magnetic fields are assumed to have been spontaneously
generated at the reheating stage of the early Universe, due to vacuum
polarization of non-Abelian gauge fields at high temperature. The fact that the
screening mass of this type of fields has zero value was discovered recently. A
procedure to estimate their field strengths, $B(T)$, at different temperatures
is here developed, and the value $B(T_{ew}) \sim 10^{14} G$ at the electroweak
phase transition temperature, is derived by taking into consideration the
present value of the intergalactic magnetic field strength, $B_0 \sim 10^{- 15}
G$, coherent on the $\sim 1$ Mpc scale. As a particular case, the standard
model is considered and the field scale at high temperature is estimated in
this case. Model dependent properties of the phenomena under investigation are
briefly discussed, too.
