The spectral asymmetry of the wave-energy distribution of dust particles during mode-coupling-induced melting, observed for the first time in plasma crystals by Couëdel et al. [Phys. Rev. E 89, 053108 (2014), 10.1103/PhysRevE.89.053108], is studied theoretically and by molecular-dynamics simulations. It is shown that an anisotropy of the well confining the microparticles selects the directions of preferred particle motion. The observed differences in intensity of waves of opposed directions are explained by a nonvanishing phonon flux. Anisotropic phonon scattering by defects and Umklapp scattering are proposed as possible reasons for the mean phonon flux.