  The problem of black body radiation, when measured by a moving observer, has
a pivotal role in relativistic thermodynamics. Mutually, it depends on the
thermodynamical definition of the thermal equilibrium and temperature of moving
bodies, i.e. under a Lorentz transformation, and also in a gravitational field.
Surprisingly, even after more than a century, relativistic thermodynamics is
not a mature theory and is still an open problem without a consensus. This
article is a brief review of the evolution of this theory with a special focus
on the black body radiation in moving frames. As an application, we use the
results in the most interesting topics of the quantum field theory in curved
space: Hawking radiation, and Unruh effect.
