  We simulate SU(2) gauge theory at temperatures ranging from slightly below
$T_c$ to roughly $2T_c$ for two different values of the gauge coupling. Using a
histogram method, we extract the effective potential for the Polyakov loop and
for the phases of the eigenvalues of the thermal Wilson loop, in both the
fundamental and adjoint representations. We show that the classical potential
of the fundamental loop can be parametrized within a simple model which
includes a Vandermonde potential and terms linear and quadratic in the Polyakov
loop. We discuss how parametrizations for the other cases can be obtained from
this model.
