  The effective potential of the order parameter for confinement is calculated
within the variational approach to the Hamilton formulation of Yang-Mills
theory. Compactifying one spatial dimension and using a background gauge fixing
this potential is obtained by minimizing the energy density for a given
constant and color diagonal background field directed along the compactified
dimension. Using Gaussian type trial wave functionals I establish an analytic
relation between the propagators in the background gauge at finite temperature
and the corresponding zero temperature propagators in Coulomb gauge. In the
simplest truncation, neglecting the ghost and using the ultraviolet form of the
gluon energy one recovers the Weiss potential. On the other hand from the
infrared form of the gluon energy one finds an effective potential which yields
a vanishing Polyakov loop indicating the confined phase. From the full
non-perturbative potential (with the ghost included) one extracts a critical
temperature of the deconfinement phase transition of 269 MeV for the gauge
group SU(2) and 283 MeV for SU(3).
