  In the celebrated Unruh effect, we learn that a uniformly accelerating
detector in a Minkowski vacuum spacetime registers a constant temperature.
Building on prior work, we present a technique based on derivative couplings of
the two-point Wightman function and the Hadamard renormalization procedure to
define an instantaneous temperature for a massive scalar field, non-minimally
coupled to gravity. We find the temperature contains local contributions from
the acceleration of the detector, the curvature of spacetime, and the
renormalized stress-energy tensor of the field. Our result, which can be
considered as a generalized Stefan-Boltzmann law for curved spacetimes, agrees
with the familiar expressions found in 4D Rindler, thermal Minkowski, and de
Sitter.
