  We study the electrical conductance in single-mode quantum wires with Rashba
spin-orbit interaction subjected to externally applied magnetic fields in the
regime in which the ratio of spin-orbit momentum to the Fermi momentum is close
to an odd integer, so that a combined effect of multi-electron interaction and
applied magnetic field leads to a partial gap in the spectrum. We study how
this partial gap manifests itself in the temperature dependence of the
fractional conductance of the quantum wire. We use two complementing techniques
based on bosonization: refermionization of the model at a particular value of
the interaction parameter and a semiclassical approach within a dilute soliton
gas approximation of the functional integral. We show how the low-temperature
fractional conductance can be affected by the finite length of the wire, by the
properties of the contacts, and by a shift of the chemical potential, which
takes the system away from the resonance condition. We also predict an internal
resistivity caused by a dissipative coupling between gapped and gapless modes.
