  We study nonequilibrium steady states of a one-dimensional stochastic model,
originally introduced as an approximation of the Discrete Nonlinear
Schr\"odinger equation. This model is characterized by two conserved
quantities, namely mass and energy; it displays a ``normal", homogeneous phase,
separated by a condensed (negative-temperature) phase, where a macroscopic
fraction of energy is localized on a single lattice site. When steadily
maintained out of equilibrium by external reservoirs, the system exhibits
coupled transport herein studied within the framework of linear response
theory. We find that the Onsager coefficients satisfy an exact scaling
relationship, which allows reducing their dependence on the thermodynamic
variables to that on the energy density for unitary mass density. We also
determine the structure of the nonequilibrium steady states in proximity of the
critical line, proving the existence of paths which partially enter the
condensed region. This phenomenon is a consequence of the Joule effect: the
temperature increase induced by the mass current is so strong as to drive the
system to negative temperatures. Finally, since the model attains a diverging
temperature at finite energy, in such a limit the energy-mass conversion
efficiency reaches the ideal Carnot value.
