  We compute the 2-loop thermal partition function of Yang-Mills theory on a
small 3-sphere, in the large N limit with weak 't Hooft coupling. We include
N_s scalars and N_f chiral fermions in the adjoint representation of the gauge
group (S)U(N), with arbitrary Yukawa and quartic scalar couplings, assuming
only commutator interactions. From this computation one can extract information
on the perturbative corrections to the spectrum of the theory, and the
correction to its Hagedorn temperature. Furthermore, the computation of the
2-loop partition function is a necessary step towards determining the order of
the deconfinement phase transition at weak coupling, for which a 3-loop
computation is needed.
