Experimental data on the thermal conductivity <$E kappa~(T)> of some simple alcohols have been compared, analyzed and generalized. The objects of investigation were methyl, protonated and deuterated ethyl, 1-propyl and 1-butyl alcohols in the thermodynamically equilibrium phase with a complete orientational order. The temperature interval was from 2 К to the melting point under the equilibrium vapor pressure. It is found that in the region above the temperature of the maximum thermal conductivity <$E kappa~(T)> deviates from the 1/T law. This is because the total thermal conductivity has an extra contribution <$E kappa sub roman II (T)> of short-lived phonons in addition to <$E kappa sub roman I~(T)> contributed by propagating phonons: <$E kappa~(T)~=~kappa sub roman I~(T)~+~kappa sub roman II~(T)>. The contribution <$E kappa sub roman I~(T)> is well described by the Debye - Peierls model allowing for the phonon - phonon processes and scattering of phonons by dislocations. At <$ET~>>~40> К the contribution <$E kappa sub roman I~(T)> obeys the law A/T and <$E kappa sub roman II~(T)> is practically temperature-independent. It is shown that the Debye temperature <$E THETA sub D> of alcohol is dependent on the molecular mass as <$E THETA sub D~=~678 M sup -0,42> К and the coefficient A characterizing the intensity of the phonon - phonon scattering increases with the molecular mass of the simple monoatomic alcohol by the law <$EA~=~0,85 M sup 0,8> W/m, which suggests a decreasing intensity of the phonon - phonon process.