  This Article investigates dissipative preparation of entangled
non-equilibrium steady states (NESS). We construct a collision model where the
open system consists of two qubits which are coupled to heat reservoirs with
different temperatures. The baths are modeled by sequences of qubits
interacting with the open system. The model can be studied in different
dynamical regimes: with and without environmental memory effects. We report
that only a certain bath temperature range allows for entangled NESS.
Furthermore, we obtain minimal and maximal critical values for the heat current
through the system. Surprisingly, quantum memory effects play a crucial role in
the long time limit. First, memory effects broaden the parameter region where
quantum correlated NESS may be dissipatively prepared and, secondly, they
increase the attainable concurrence. Most remarkably, we find a heat current
range that does not only allow but guarantees that the NESS is entangled. Thus,
the heat current can witness entanglement of non-equilibrium steady states.
