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We investigate the thermodynamic properties of 3+1 dimensional black holes inasymptotically de Sitter spacetimes, conformally coupled to a real scalarfield. We use a Euclidean action approach, where boundary value data isspecified at a finite radius `cavity' outside the black hole, working in theextended phase space where the cosmological constant is treated as athermodynamic pressure. We examine the phase structure of these black holesthrough their free energy. For the MTZ subclass of solutions, we findHawking-Page-like phase transitions from a black hole spacetime to thermal deSitter with a scalar field. In the more general case, Hawking-Page-like phasetransitions are also present, whose existence depends further on a particularcosmic censorship bound.

Thermodynamics of de Sitter Black Holes with Conformally Coupled Scalar Fields