  The Unruh effect, predicting a thermal reservoir for accelerating systems,
calls for a more refined understanding of measurement processes involving
quantum systems as thermometers. Conventional models fail to account for the
inherent spatial extent of the thermometer, neglecting the complexities
associated with accelerated extended quantum systems. Our work builds upon the
seminal work of Bell, Hughes, and Leinaas. We propose a refined thermometer
model incorporating a spin-1/2 particle where the spin acts as a temperature
indicator. This refined model demonstrates the ability to effectively measure
the temperature under specific, realistic conditions, providing a unique value
that essentially averages the local Unruh temperatures throughout the extended
quantum system acting as the thermometer.
