  The Coulomb gauge model of QCD is studied with the introduction of a
confining potential into the scalar part of the vector potential. Using a Green
function formalism, we derive the self-energy for this model, which has both
scalar and vector parts, $\Sigma^S(p)$ and $\Sigma^V(p)$. A rotation of these
variables leads to the so-called gap and energy equations. We then analyse the
divergence structure of these equations. As this depends explicitly on the form
of potential, we give as examples both the linear plus Coulomb and
quadratically confining potentials. The nature of the confining single particle
Green function is investigated, and shown to be divergent due to the infrared
singularities caused by the confining potential. Solutions to the gap equation
for the simpler case of quadratic confinement are found both semi-analytically
and numerically. At finite temperatures, the coupled set of equations are
solved numerically in two decoupling approximations. Although chiral symmetry
is found only to be exactly restored as $T\to\infty$, the chiral condensate
displays a steep drop over a somewhat small temperature range.
