  We analyse the thermodynamics of a quantum system in a trajectory of constant
velocity that interacts with a static thermal bath. The latter is modeled by a
massless scalar field in a thermal state. We consider two different couplings
of the moving system to the heat bath, a coupling of the Unruh-DeWitt type and
a coupling that involves the time derivative of the field. We derive the master
equation for the reduced dynamics of the moving quantum system. It has the same
form with the quantum optical master equation, but with different coefficients
that depend on velocity. This master equation has a unique asymptotic state for
each type of coupling, and it is characterized by a well-defined notion of
heat-flow. Our analysis of the second law of thermodynamics leads to a
surprising equivalence: a moving heat bath is physically equivalent to a
mixture of heat baths at rest, each with a different temperature. There is no
unique rule for the Lorentz transformation of temperature. We propose that
Lorentz transformations of thermodynamic states are well defined in an extended
thermodynamic space that is obtained as a convex hull of the standard
thermodynamic space.
