A simple model is presented that describes the complex behavior of the magnetic field dependence of the thermal conductivity of a polyatomic gas as a function of the Knudsen number. The model treats the solid surface as one component of a gas mixture, and a first-order Chapman-Enskog solution is adequate to account for the thermomagnetic effects in single gases. The results provide an interpolation scheme between the continuum and Knudsen regimes, in the form of scaling rules in which the Knudesen number appears in the coefficients and arguments of the functions that describe the limiting cases. Good agreement is obtained with the available experimental data, and leads to the conclusion that different surface accommodation coefficients are needed for the translational and internal energies of the gas molecules. This conclusion is consistent with analysis of independent field-free conductivity data, and with independent vibrating-surface measurements.