In this work, we propose a practical implementation of a two-qubit entanglement engine on a Nitrogen-Vacancy (NV) center platform. This engine for dissipation-induced entanglement generation relies on two interacting artificial atoms, coupled independently to two thermally biased environments. In our scheme, the role of the qubits is played by the electron spin transitions of two NV centers, coupled through a dipole-dipole interaction. Independently from the phononic temperature, the surrounding Carbon 13 nuclear spins play the role of thermal environments. Importantly, we show that a dissipative process can dominate the qubit-bath dynamics over decoherence. We highlight that recent progresses in Dynamical Nuclear Polarization combined with microscopy superresolution methods allow us to initialize a long lasting out-of-equilibrium polarization situation between two spin baths, independently coupled to each NV-center qubit. The transient and steady-state dynamics is investigated within a master equation framework. Entanglement is predicted between the electron spins of two nearby NV centers under realistic experimental conditions.