The conductance of a 20 μm long quantum wire in an AlGaAs/GaAs heterostructure is investigated as a function of a perpendicular magnetic field and the temperature. Quantization in units of 2e²/h occurs at moderate field strengths and sufficiently low temperatures. For higher magnetic fields an additional conductance plateau at e²/h occurs due to an exchange-interaction-induced Zeeman splitting of the corresponding subband. With increasing temperature, the conductance plateaus are partially reduced, which is characteristic for the interaction between the electrons and three-dimensional phonons. The interpretation is based on an enhancement of the electron-phonon scattering as soon as the Fermi velocity within a subband exceeds the sound velocity. Within the region of strong scattering the temperature dependence of the conductance changes from T³ to T.