The thermal conductivity of crystals of holmium ethylsulphate has been measured in the range 1 to 4.25 $^\circ$K in zero magnetic field and also in fields up to 53 kG, applied parallel to the hexagonal axis. The change in the thermal resistivity in a field is characterized by two maxima separated by a local, temperature-independent minimum at ca. 5.5 kG and another one, observable at 3 $^\circ$K and above at ca. 17 kG. The resistivity in very high fields is constant and is lower than that in zero field. The 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 field. A good quantitative fit to the experimental data is only obtained by calculating the total thermal resistivity (including boundary and point defect scattering) rather than the individual contribution due to spin scattering alone. A statistical model is used which takes account of the relative populations of the various energy levels and assumes a Gaussian lineshape for them. The line widths and the relative transition probabilities between the levels may be estimated from the theory since the calculations are very sensitive to the values of these parameters.