Thermodynamics of de Sitter black holes with conformally coupled scalar fields

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