  We discuss the glueball contribution to the equation of state (EoS) of hot
gluon matter below and above $T_c$. It is shown that the strong changing of
masses of scalar and pseudoscalar glueballs near $T_c$ plays very important
role in the thermodynamics of $SU(3)$ gauge theory. In particular, we give the
arguments that these glueballs become massless at $T_G\approx 1.1T_c$ and this
phenomenon is crucial in understanding of the mystery in the behavior of trace
anomaly founded in the lattice calculation.
