  The effective potential approach for composite operators has been generalized
to non-zero temperatures in order to derive equation of state for the pure
SU(3) Yang-Mills fields from first principles. In the absence of external
sources it is nothing but the vacuum energy density. The key element of this
derivation was an introduction of the temperature dependence into the
expression for the Bag constant. Such obtained non-perturbative analytical
equation of state for the gluon matter does not depend on the coupling
constant, only the dependence on the mass gap, which is responsible for the
large-scale structure of the QCD ground state, is present. The important
thermodynamic quantities such as the pressure, energy and entropy densities,
etc. have been calculated. We have shown explicitly that the pressure may
continuously change its regime at $T_c=266.5 Mev$. All other thermodynamic
quantities are to be understood to have drastic changes in their regimes at
this point. The proposed analytical approach makes it possible to controll
thermodynamics of the gluon matter at low temperatures below $T_c$ for the
first time. We automatically reproduce the so-called "fuzy"-type bag models
properties because of the mass gap explicit presence in our equation of state.
We have also analytically calculated the NP gluon condensate as a function of
temperature.
