  We study the role of dipolar interactions in the standard protocol used to
achieve dynamic nuclear polarization (DNP). In the so-called spin-temperature
regime, where the interactions establish an effective thermodynamic behavior in
the out-of-equilibrium stationary state, we provide numerical predictions for
the level of hyperpolarization. We show that nuclear spins equilibrate to the
effective spin-temperature established among the electron spins of radicals, as
expected from the quantum theory of thermalization. Moreover, we present an
analytical technique to estimate the spin temperature, and thus, the nuclear
hyperpolarization in the steady state, as a function of interaction strength
and quenched disorder. This reproduces both our numerical data and experimental
results. Our central finding is that the nuclear hyperpolarization increases
steadily upon reducing the interaction strength (by diluting the radical
density). Interestingly, the highest polarization is reached at a point where
the establishment of a spin temperature is just about to break down due to the
incipient many-body localization transition in the electron spin system.
