  We construct matrix models for the deconfining phase transition in SU(N)
gauge theories, without dynamical quarks, at a nonzero temperature T. We
generalize models with zero and one free parameter to study a model with two
free parameters: besides perturbative terms ~T^4, we introduce terms ~T^2 and
~T^0. The two N-dependent parameters are determined by fitting to data from
numerical simulations on the lattice for the pressure, including the latent
heat. Good agreement is found for the pressure in the semi-quark gluon plasma
(QGP), which is the region from Tc, the critical temperature, to about ~4 Tc.
Above ~1.2 Tc, the pressure is a sum of a perturbative term, ~ +T^4, and a
simple non-perturbative term, essentially just a constant times ~ -Tc^2 T^2.
For the pressure, the details of the matrix model only enter within a very
narrow window, from Tc to ~1.2 Tc, whose width does not change significantly
with N. Without further adjustment, the model also agrees well with lattice
data for the 't Hooft loop. This is notable, because in contrast to the
pressure, the 't Hooft loop is sensitive to the details of the matrix model
over the entire semi-QGP. For the (renormalized) Polyakov loop, though, our
results disagree sharply with those from the lattice. Matrix models provide a
natural and generic explanation for why the deconfining phase transition in
SU(N) gauge theories is of first order not just for three, but also for four or
more colors. Lastly, we consider gauge theories where there is no strict order
parameter for deconfinement, such as for a G(2) gauge group. To agree with
lattice measurements, in the G(2) matrix model it is essential to add terms
which generate complete eigenvalue repulsion in the confining phase.
