  Thermodynamical stability of fluid spheres is studied in the presence of a
cosmological constant, both in the Newtonian limit, as well as in General
Relativity. In all cases, an increase of the cosmological constant tends to
stabilize the system, making asymptotically de Sitter space more
thermodynamically stable than anti-de Sitter at the purely classical level. In
addition, in the Newtonian case reentrant phase transitions are observed for a
positive cosmological constant, due to its repelling property in this case. In
General Relativity is studied the case of radiation, for which is found that
the critical radius, at which an instability sets in, is always bigger than the
black hole radius of the system and furthermore, at some value of the
cosmological constant this critical radius hits at the cosmological horizon.
