Using the relaxation time approach, the authors present a new analysis of phonon conductivity which shows that at high temperature (T> theta _D, the Debye temperature), the longitudinal phonons are the dominant heat carriers in germanium. The present result, which is a consequence of the effect of phonon dispersion on the Callaway integral for lattice thermal conductivity, is contrary to the general belief that transverse phonons carry heat at T> theta _D. A qualitative justification has also been given for the three-phonon scattering parameters obtained.