  A physically meaningful local concept of temperature is introduced in quantum
field theory on curved spacetime and applied to the example of a massless field
on de Sitter space. It turns out in this model that the equilibrium (Gibbs)
states which can be prepared by a geodesic observer have in general a varying
temperature distribution in the neighborhood of the geodesic and may not even
allow for a consistent thermal interpretation close to the horizon. This
result, which can be traced back to the Unruh effect, illustrates the failure
of a global notion of temperature in curved spacetime and reveals the need for
a local concept, as presented here.
