The thermal conductivity of crystals of concentrated cerium ethylsulphate has been measured in the range 1 to 4.58 $^\circ$K and in magnetic fields of up to 53 kG. In zero field there is a marked anomaly at 2.5 $^\circ$K in the variation of conductivity with temperature. Owing to the anisotropy of the g-values the magnetic field dependence of the thermal resistivity at constant temperature depends on the field direction; with the field parallel to the hexagonal axis, a maximum occurs in the resistivity which moves roughly linearly with temperature, and in very high fields it is always less than in zero field; with the field applied in the perpendicular direction a resistivity maximum is only observed above 2 $^\circ$K, and in the highest available field it is always much greater than in zero field. These results are explained by assuming that direct process phonon-spin interactions scatter certain bands of phonons whose frequency depends on the separation of the energy levels produced by the applied magnetic field. A statistical theory is used to determine the relative populations of the energy levels in the calculation of the thermal resistivity. It is assumed that the spin-phonon absorption lineshape is Gaussian. By fitting the theory to the experimental data, approximate values of the spin-lattice coupling constant, the linewidth of the transitions and the mean free paths for boundary and point-defect scattering are obtained.