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By utilizing the theoretical tools of optical thermodynamics, we investigate thermalization in nonlinear disordered lattices beyond the diffusion regime. Even under extreme levels of disorder, we analytically predict the expected thermal value of entropy and the associated Rayleigh-Jeans distribution, once thermalization ensues. In this context, we reveal a crossover point of disorder beyond which we observe a pronounced slowdown of thermalization in a regime characterized by a logarithmic scaling of equilibration times. By employing the same analytical and numerical tools, we investigate the scaling of thermalization times with respect to both the number of sites and optical temperatures. By exploring the physics of the underlying nonequilibrium response, we unveil a multitude of emerging thermal phenomena, including the development of prethermal Rayleigh-Jeans states in the presence of an optical heat bath and the deceleration of self-heating in Floquet photonic lattices.