  We study the temperature dependence of the electrical conductance of a clean
strongly interacting quantum wire in the presence of a helical nuclear spin
order. The nuclear spin helix opens a temperature-dependent partial gap in the
electron spectrum. Using a bosonization framework we describe the gapped
electron modes by sine-Gordon-like kinks. We predict an internal resistivity
caused by an Ohmic-like friction these kinks experience via interacting with
gapless excitations. As a result, the conductance rises from $G=e^2/h$ at
temperatures below the critical temperature when nuclear spins are fully
polarized to $G=2e^2/h$ at higher temperatures when the order is destroyed,
featuring a relatively wide plateau in the intermediate regime. The theoretical
results are compared with the experimental data for GaAs quantum wires obtained
recently by Scheller et al. [Phys. Rev. Lett. 112, 066801 (2014)].
