The thermodynamics of homogeneous isotropic universes (kg0, \ensuremath{\Lambda}g0) with conformal scalar radiation is analyzed, in analogy with the thermodynamics of black holes in a cavity, as the mutual equilibrium between two subsystems (quantum thermal bosons and semiclassical conformal metric modes) fluctuating under an energy constraint corresponding to the analytic continuation of one of Einstein's equations. The global stability of the cosmological thermal state previously deduced from a statistical computation is confirmed, while the (de Sitter) vacuum state turns out to be locally unstable to creation and heating of matter, and can decay, by an irreversible quasistatic process of energy extraction from gravity, to the equilibrium state compatible with an inflationary cosmology.