  We propose a quasiparticle approach allowing to compute the equation of state
of a generic gauge theory with gauge group SU($N_c$) and quarks in an arbitrary
representation. Our formalism relies on the thermal quasiparticle masses
(quarks and gluons) computed from Hard-Thermal-Loop techniques, in which the
standard two-loop running coupling constant is used. Our model is minimal in
the sense that we do not allow any extra ansatz concerning the
temperature-dependence of the running coupling. We first show that it is able
to reproduce the most recent equations of state computed on the lattice for
temperatures higher than 2 $T_c$. In this range of temperatures, an ideal gas
framework is indeed expected to be relevant. Then we study the accuracy of
various inequivalent large-$N_c$ limits concerning the description of the QCD
results, as well as the equivalence between the QCD$_{AS}$ limit and the ${\cal
N}=1$ SUSY Yang-Mills theory. Finally, we estimate the dissociation temperature
of the $\Upsilon$-meson and comment on the estimations' stability regarding the
different considered large-$N_c$ limits.
