  The thermodynamics of supersymmetric Yang-Mills theories is studied by
computing the two-loop correction to the canonical free energy and to the
equation of state for theories with 16, 8 and 4 supercharges in any dimension
$4\leq d\leq 10$, and in two dimensions at finite volume. In the
four-dimensional case we also evaluate the first non-analytic contribution in
the 't Hooft coupling to the free energy, arising from the resummation of ring
diagrams. To conclude, we discuss some applications to the study of the
Hagedorn transition in string theory in the context of Matrix strings and
speculate on the possible physical meaning of the transition.
