  Path integral Monte Carlo simulation of the dipositronium "molecule" Ps$_2$
reveals its surprising thermal instability. Although, the binding energy is
$\sim 0.4$ eV, due to the strong temperature dependence of its free energy
Ps$_2$ dissociates, or does not form, above $\sim 1000$ K, except for high
densities where a small fraction of molecules are in equilibrium with Ps atoms.
This prediction is consistent with the recently reported first observation of
stable Ps$_2$ molecules by Cassidy & Mills Jr., Nature {\bf 449}, 195 (07), and
Phys.Rev.Lett. {\bf 100}, 013401 (08); at temperatures below 1000 K. The
relatively sharp transition from molecular to atomic equilibrium, that we find,
remains to be experimentally verified. To shed light on the origin of the large
entropy factor in free energy we analyze the nature of interatomic interactions
of these strongly correlated quantum particles. The conventional diatomic
potential curve is given by the van der Waals interaction at large distances,
but due to the correlations and high delocalization of constituent particles
the concept of potential curve becomes ambiguous at short atomic distances.
