  We study numerically the chromoelectric-chromomagnetic asymmetry of the
dimension two $A^2$ gluon condensate as well as the infrared behavior of the
gluon propagators at $T\simeq T_c$ in the Landau-gauge $SU(3)$ lattice gauge
theory. We find that a very significant correlation of the real part of the
Polyakov loop with the asymmetry as well as with the longitudinal propagator
makes it possible to determine the critical behavior of these quantities. We
obtain the screening masses in different Polyakov-loop sectors and discuss the
dependence of chromoelectric and chromomagnetic interactions of static color
charges and currents on the choice of the Polyakov-loop sector in the
deconfinement phase.
