  We study a pure gluon plasma in the context of quasiparticle models, where
the plasma is considered as an ideal gas of massive bosons. In order to
reproduce SU(3) gauge field lattice data within such a framework, we review
briefly the necessity to use a temperature-dependent gluon mass which accounts
for color interactions between the gluons near $T_{\text{c}}$ and agrees with
perturbative QCD at large temperatures. Consequently, we discuss the
thermodynamics of systems with temperature-dependent Hamiltonians and clarify
the situation about the possible solutions proposed in the literature to treat
consistently those systems. We then focus our attention to two possible
formulations which are thermodynamically consistent and we extract the gluon
mass from the equation of state obtained in SU(3) lattice QCD. We find that the
thermal gluon mass is similar in both statistical formalisms. Finally, an
interpretation of the gluon plasma as an ideal gas made of glueballs and gluons
is also presented. The glueball mass is consistently computed within a
relativistic formalism using a potential obtained from lattice QCD. We find
that the gluon plasma might be a glueball-rich medium for $T\lesssim 1.13
T_{\text{c}}$ and suggest that glueballs could be detected in future
experiments dedicated to the quark-gluon plasma.
