Existing methods of estimating spatially varying soil thermal conductivity and diffusivity using harmonic analysis of soil temperatures are applicable only at periodic steady state. This study adopted a more general Fourier analysis which is applicable when transients are present. Two new methods of estimation were compared with existing methods using synthetic data generated by solution of the one-dimensional heat conduction equation in a soil whose water content varied with depth. All methods gave accurate results for the logarithmic derivative of conductivity and the diffusivity at steady state, but only the new methods were accurate when initial temperatures led to transients. Sensitivity to depth spacings and to noise were also investigated. Spatially interpolating the amplitude and phase of the temperature data with filtering for estimating derivatives allowed good results to be obtained in the presence of noise, especially for the diffusivity. Although the methods work best for temperatures at several depths and spacings of 0.05 m or less, errors in diffusivity were less than 8% with only three depths at 0.1 m spacing.