The unruh process is asymmetric. The inertial observer is in his vacuum V0 and the accelerated observer measures $\langle V_0|N|V_0 \rangle$ and sees particles. He is not in his vacuum environment. I wonder if the accelerared observer can act locally on it to get a limited space time region in his vacuum V'? If he can do that what does the inertial observer "see" in this regieon ? particles ? antiparticles? nothing? thanks.
Edit: My question is not about the usual unruh effect. it is not about the accelerated thermometer and why it is like that. I wonder if the inertial thermometer would still indicate a zero temperature in a given spacetime region in which the accelerated observer would be in his vacuum $V_{acc}$