  In this paper we compute the temperature registered by an Unruh-DeWitt
detector coupled to a Hadamard renormalizable quantum field in an arbitrary
state, moving along an accelerated trajectory in a curved spacetime. For a
massless and conformally invariant field, the generalized expression for the
temperature is given by the quadratic sum of the 4-acceleration, Raychaudhuri
scalar, and renormalized field polarization. We can further find a novel
constraint on the renormalized quantum field polarization in relativistic
systems that are in global thermal equilibrium.
