  Using a parametrization of the Wilson loop with the minimal-area law, we
calculate the polarization operator of a valence gluon, which propagates in the
confining background. This enables us to obtain the infrared freezing (i.e.
finiteness) of the running strong coupling in the confinement phase, as well as
in the deconfinement phase up to the temperature of dimensional reduction. The
momentum scale defining the onset of freezing is found both analytically and
numerically. The nonperturbative contribution to the thrust variable,
originating from the freezing, makes the value of this variable closer to the
experimental one.
