  We study the conductance of a quantum wire in the presence of weak
electron-electron scattering. In a sufficiently long wire the scattering leads
to full equilibration of the electron distribution function in the frame moving
with the electric current. At non-zero temperature this equilibrium
distribution differs from the one supplied by the leads. As a result the
contact resistance increases, and the quantized conductance of the wire
acquires a quadratic in temperature correction. The magnitude of the correction
is found by analysis of the conservation laws of the system and does not depend
on the details of the interaction mechanism responsible for equilibration.
