  We consider two separated oscillators initially in equilibrium and
continuously interacting with thermal environments, and propose a way to
entangle them using a mediating qubit. An appropriate interaction allows for an
analytic treatment of the open system, removes the necessity of fine-tuning
interaction times and results in a high tolerance of the entanglement to finite
temperature. The entanglement thus produced between the oscillators can be
verified either through a Bell inequality relying on oscillator parity
measurements or through conditional extraction of the entanglement on to two
mutually non-interacting qubits. The latter process also shows that the
generated mixed entangled state of the oscillators is an useful resource for
entangling qubits. By allowing for influences from environments, taking
feasible qubit-oscillator interactions and measurement settings, this scheme
should be implementable in a variety of experimental setups. The method
presented for the solution of the master equation can also be adapted to a
variety of problems involving the same form of qubit-oscillator interaction
