We test ideas of the recently proposed first-order thermodynamics of scalar-tensor gravity using an exact geometry sourced by a conformally coupled scalar field. We report a nonmonotonic behavior of the effective ``temperature of gravity'' not observed before and due to a new term in the equation describing the relaxation of gravity toward its state of equilibrium, i.e., Einstein gravity, showing a richer range of thermal behaviors of modified gravity than previously thought.
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Karolinski et al. (2024) studied this question.
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