  We study the thermalization of smeared particle detectors that couple locally
to $any$ operator in a quantum field theory in curved spacetimes. We show that
if the field state satisfies the KMS condition with inverse temperature $\beta$
with respect to the detector's local notion of time evolution, reasonable
assumptions ensure that the probe thermalizes to the temperature $1/\beta$ in
the limit of long interaction times. Our method also imposes bounds on the size
of the system with respect to its proper acceleration and spacetime curvature
in order to accurately probe the KMS temperature of the field. We then apply
this formalism to a uniformly accelerated detector probing the Minkowski vacuum
of any CPT symmetric quantum field theory, and show that the detector
thermalizes to the Unruh temperature, independently of the operator it couples
to. This exemplifies yet again the robustness of the Unruh effect, even when
arbitrary smeared detectors are used to probe general operators in a quantum
field theory.
