  We study the effect of thermal equilibration on the transport properties of a
weakly interacting one-dimensional electron system. Although equilibration is
severely suppressed due to phase-space restrictions and conservation laws, it
can lead to intriguing signatures in partially equilibrated quantum wires. We
consider an ideal homogeneous quantum wire. We find a finite temperature
correction to the quantized conductance, which for a short wire scales with its
length, but saturates to a length-independent value once the wire becomes
exponentially long. We also discuss thermoelectric properties of long quantum
wires. We show that the uniform quantum wire is a perfect thermoelectric
refrigerator, approaching Carnot efficiency with increasing wire length.
