  We show that a single nonlinear defect can thermalize an initial excitation
towards a Rayleigh-Jeans (RJ) state in complex multimoded systems. The
thermalization can be hindered by disorder-induced localization phenomena which
drive the system into a metastable RJ state. It involves only a
(quasi-)isolated set of prethermal modes and can differ dramatically from the
thermal RJ. We develop a one-parameter scaling theory that predicts the density
of prethermal modes and we derive the modal relaxation rate distribution,
establishing analogies with the Thouless conductance. Our results are relevant
to photonics, optomechanics, and cold atoms.
