  We investigate whether inertial thermometers moving in a thermal bath behave
as being hotter or colder. This question is directly related to the classical
controversy concerning how temperature transforms under Lorentz
transformations. Rather than basing our arguments on thermodynamical
hypotheses, we perform straightforward calculations in the context of
relativistic quantum field theory. For this purpose we use Unruh-DeWitt
detectors, since they have been shown to be reliable thermometers in
semi-classical gravity. We believe that our discussion helps in definitely
clarifying this issue.
