For unpolarized electrons in a clean quantum wire, density functional theory reveals a thermally activated suppression of conductance. The activation temperature T_A grows slowly (roughly quadratically) with gate voltage due to pinning of the band edge at the chemical potential. Similar results were obtained experimentally by Kristensen et al. [Phys. Rev. B62, 10950 (2000)] for the temperature dependence of the anomalous conductance plateau near 0.7 (2e^2/h) in a quantum point contact.