  In this paper we provide an exact formula for the area law of the 't Hooft
loop for any SU(N) gauge group to cubic order in hot gauge theory.
  The correction is very small for all temperatures above $T_c$, in stark
contrast to the cubic correction to the pressure. The gradient approximation in
a previous paper, only valid for large N, is in excellent agreement with the
present, exact evalution. Comparison to lattice data is good. Casimir scaling
is violated by a small amount not yet resolved by the precision of lattice
data.
