Better methods of estimating soil thermal conductivity and diffusivity from temperature measurements taken in practical situations where the thermal properties vary spatially will aid both soil science and engineering. In recently published work, I presented a method for estimating these properties when they vary vertically and the system may not be in the periodic steady state. This study extended that analysis to two and three dimensions. Using numerical solutions of the heat equation for conduction in inhomogeneous solids, synthetic temperatures were generated on a fine spatial grid and used to verify that the methods were accurate for daily periods, even in the absence of the periodic steady state. Errors due to increasing the spacing of the generated temperatures and to ignoring lateral variations were investigated. Temperatures on coarser grids led to errors that ranged up to a maximum of 20% at spacings of 0.25 m laterally and 0.1 m vertically when thermal conductivity varied fourfold in one lateral direction and ninefold vertically. In contrast, one-dimensional analyses on a fine grid with 0.01-m spacing produced errors of up to 54% that decreased to 7% when conductivity changed laterally by a factor of 1.2 instead of four. This error could be reduced by inclusion of a few lateral temperatures. Analysis of synthetic data that included a sharp spatial transition in thermal properties showed that the method would still be applicable where abrupt changes of soil material or water content occur.