  We theoretically investigate a weakly-interacting degenerate Bose gas coupled
to an empty Markovian bath. We show that in the universal phononic limit the
system evolves towards an asymptotic state where an emergent temperature is set
by the quantum noise of the outcoupling process. For situations typically
encountered in experiments, this mechanism leads to significant cooling. Such
dissipative cooling supplements conventional evaporative cooling and dominates
in settings where thermalization is highly suppressed, such as in a
one-dimensional quasicondensate.
