  With insight from examples and physical arguments, the Tolman-Ehrenfest
criterion of thermal equilibrium for test fluids in static spacetimes is
extended to local thermal equilibrium in conformally static geometries. The
temperature of the conformally rescaled fluid scales with the inverse of the
conformal factor, reproducing the evolution of the cosmic microwave background
in Friedmann universes, the Hawking temperature of the Sultana-Dyer
cosmological black hole, and a heuristic argument by Dicke.
