  We consider N = 4 supersymmetric Yang-Mills theory with SU(N) gauge group at
large N and at finite temperature on a spatial S^3. We show that, at finite
weak 't Hooft coupling, the theory is naturally described as a two dimensional
Coulomb gas of complex eigenvalues of the Polyakov-Maldacena loop, valued on
the cylinder. In the low temperature confined phase the eigenvalues condense
onto a strip encircling the cylinder, while the high temperature deconfined
phase is characterised by an ellipsoidal droplet of eigenvalues.
