We study an ensemble of two-level quantum systems (qubits) interacting with a common electromagnetic field in the proximity of a dielectric slab whose temperature is held different from that of some far surrounding walls. We show that the dissipative dynamics of the qubits driven by this stationary and out of thermal equilibrium field allows the production of steady many-body entangled states, different from the case at thermal equilibrium where steady states are always nonentangled. By studying up to ten qubits, we point out the role of symmetry in the entanglement production, which is exalted in the case of permutationally invariant configurations. In the case of three qubits, we find a strong dependence of tripartite entanglement on the spatial disposition of the qubits, and in the case of six qubits we find several highly entangled bipartitions where entanglement can, remarkably, survive for large qubit-qubit distances up to 100 μm.