  The notion of thermal time has been introduced as a possible basis for a
fully general-relativistic thermodynamics. Here we study this notion in the
restricted context of stationary spacetimes. We show that the Tolman-Ehrenfest
effect (in a stationary gravitational field, temperature is not constant in
space at thermal equilibrium) can be derived very simply by applying the
equivalence principle to a key property of thermal time: at equilibrium,
temperature is the rate of thermal time with respect to proper time - the
`speed of (thermal) time'. Unlike other published derivations of the
Tolman-Ehrenfest relation, this one is free from any further dynamical
assumption, thereby illustrating the physical import of the notion of thermal
time.
