Measurements of anisotropic thermal diffusivity and of the velocity of hypersound have been performed at room temperature on one set of stretched low density polyethylene (crystallinityvc=0.4). The elastic anisotropy increases with the stretching ratio λ as does the heat conduction anisotropy. It is argued that the heat conduction cannot be traced back to properties of extended crystalline and amorphous phases. The reason for the latter is the smallness of the microphases giving rise only to non-propagating modes. Phonon focussing of superstructure phonons together with the wavelength dependence of their scattering can explain the observed effects. From the parameters found and from a semiquantitative description of the temperature dependence down to 4 K it is concluded that the main transport could be due to hopping mechanisms where the localized phonons may be fractons. It is conjectured that the energy flow is assisted or triggered by the long wave length phonons via anharmonic coupling giving rise to the dependence on direction.