  In high temperature SU(2) gluodynamics, in a relativistic background
R^{ext.}_xi gauge, the effective color charge (g^2(A_0))_eff. is calculated in
the presence of the A_0 condensate which is related to Polyakov's loop and also
serves as the order parameter of the deconfinement phase transition at high
temperature. The gauge-invariant value of the condensate ((A_0)^cl)_0 is
obtained from the two-loop effective potential of order parameter W_L(A_0^cl)
which is independent of the gauge-fixing parameter xi and has a nontrivial
minimum position. Due to smallness of the expansion parameter ~ g^2/(8 pi^2),
this potential is applicable at high temperatures beginning from the
deconfinement temperature T_d. The effective charge accounts for a correlation
between the one- and the two-loop terms of the W_L(A_0^cl). It results in
decreasing of the effective gluon interactions in the plasma, compared to the
zero condensate case. Temperature dependence of (g^2(A_0))_eff. is
investigated. The importance of the found dependence for different applications
is noted.
