  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.
