  We calculate the finite-temperature conductance of clean, weakly interacting
one-dimensional quantum wires subject to Rashba spin-orbit coupling and a
magnetic field. For chemical potentials near the center of the Zeeman gap ($\mu
= 0$), two-particle scattering causes the leading deviation from the quantized
conductance at finite temperatures. On the other hand, for $|\mu| > 0$,
three-particle scattering processes become more relevant. These deviations are
a consequence of the strongly nonlinear single-particle spectrum, and are thus
not accessible using Luttinger liquid theory. We discuss the observability of
these predictions in current experiments on InSb nanowires and in "spiral
liquids", where a spontaneous ordering of the nuclear spins at low temperatures
produces an effective Rashba coupling.
