Thermal instability in a gravity-like scalar theory
  We study the question of stability of the ground state of a scalar theory which is a generalization of the phi^3 theory and has some similarity to gravity with a cosmological constant. We show that the ground state of the theory at zero temperature becomes unstable above a certain critical temperature, which is evaluated in closed form at high temperature. 
F. T. Brandt, Ashok Das, J. Frenkel