  A new thermodynamics of scalar-tensor gravity is applied to spatially
homogeneous and isotropic cosmologies in this class of theories and tested on
analytical solutions. A forever-expanding universe approaches the Einstein
"state of equilibrium" with zero effective temperature at late times and
departs from it near spacetime singularities. "Cooling" by expansion and
"heating" by singularities compete near the Big Rip, where it is found that the
effective temperature diverges in the case of a conformally coupled scalar
field.
