Finite temperature Monte Carlo simulations of the SU (2) Yang-Mills system on the lattice are used to obtain an estimate of the mass m G of the lowest gluonium state. Taking gluon matter in the hadronic regime, below the deconfinement transition, to follow the usual string or bag model pattern, we find from the temperature dependence of the energy density and of the specific heat that m G = (1.7 ± 0.5)x/~, where o is the string tension.Monte Carlo studies of the SU(2) Yang-Mills system on the lattice at finite physical temperature T have revealed a deconfinement transition [1][2][3] at the critical temperature T c ~ 0.5 x,~, where the system changes from gluonium matter to gluon gas; here a denotes the strong tension. Above Tc, at sufficiently high temperatures, this gluon gas attains the (parameter-free) Stefan-Boltzmann limit of an ideal massless boson gas [3]. Below Tc, the behaviour of the system is less well understood; but if we believe that it also provides there a reasonable approximation to the real quark-ghion world, then we expect gluonium matter to exhibit the same basic features as hadron matter.The description of hadrons as bound states of quarks leads to a resonance spectrum, starting with a lowest state of mass m 0. In the continuum, both bag for an ideal gas of resonances, or its derivatives, become singular at the temperature T c = 1/b; above Tc, the integral (2) is no longer defined. If we identify this critical behaviour with the deconfinement transition of the SU(2) lattice problem at T c = 0.5 x/o, then the approach to deconfinement is governed by the lowest gluonium mass m 0 = m o as scale. Comparing the form predicted by eq. (1) with that obtained from the Monte Carlo simulation of the SU(2) Yang-Mills system thus gives an estimate of the glueball mass m G . We note that this approach -using the resonance 332 0 031-9163/81/0000-0000/$ 02.50