In one-dimensional electronic systems with strong repulsive interactions, charge excitations propagate much faster than spin excitations. Such systems therefore have an intermediate temperature range [termed the spin-incoherent Luttinger liquid (SILL) regime] where charge excitations are cold (i.e., have low entropy) whereas spin excitations are hot. We explore the effects of charge-sector disorder in the SILL regime in the absence of external sources of equilibration. We argue that the disorder localizes all charge-sector excitations; however, spin excitations are protected against full localization, and act as a heat bath facilitating charge and energy transport on asymptotically long timescales. The charge, spin, and energy conductivities are widely separated from one another. The dominant carriers of energy are neither charge nor spin excitations, but neutral phonon modes, which undergo an unconventional form of hopping transport that we discuss. We comment on the applicability of these ideas to experiments and numerical simulations.
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