  We extend our earlier investigation of the finite temperature deconfinement
transition in SU(N) gauge theories, with the emphasis on what happens as N->oo.
We calculate the latent heat in the continuum limit, and find the expected
quadratic in N behaviour at large N. We confirm that the phase transition,
which is second order for SU(2) and weakly first order for SU(3), becomes
robustly first order for N>3 and strengthens as N increases. As an aside, we
explain why the SU(2) specific heat shows no sign of any peak as T is varied
across what is supposedly a second order phase transition. We calculate the
effective string tension and electric gluon masses at T=Tc confirming the
discontinuous nature of the transition for N>2. We explicitly show that the
large-N `spatial' string tension does not vary with T for T<Tc and that it is
discontinuous at T=Tc. For T>Tc it increases as T-squared to a good
approximation, and the k-string tension ratios closely satisfy Casimir Scaling.
Within very small errors, we find a single Tc at which all the k-strings
deconfine, i.e. a step-by-step breaking of the relevant centre symmetry does
not occur. We calculate the interface tension but are unable to distinguish
between linear or quadratic in N variations, each of which can lead to a
striking but different N=oo deconfinement scenario. We remark on the location
of the bulk phase transition, which bounds the range of our large-N
calculations on the strong coupling side, and within whose hysteresis some of
our larger-N calculations are performed.
