Cylindrical Li-ion cells have demonstrated among the highest power density of all Li-ion cell types and typically employ a spiral electrode assembly. This spiral assembly is expected to cause large anisotropy in thermal conductance between the radial and axial directions due to the large number of interfaces between electrode and electrolyte layers in the radial conduction path, which are absent in the axial direction. This paper describes a novel experimental technique to measure the anisotropic thermal conductivity and heat capacity of Li-ion cells using adiabatic unsteady heating. Analytical modeling of the method is presented and is shown to agree well with finite-element simulation models. Experimental measurements indicate that radial thermal conductivity is two orders of magnitude lower than axial thermal conductivity for cylindrical 26650 and 18650 LiFePO4 cells. Due to the strong influence of temperature on cell performance and behavior, accounting for this strong anisotropy is critical when modeling battery behavior and designing battery cooling systems. This work improves the understanding of thermal transport in Li-ion cells, and presents a simple method for measuring anisotropic thermal transport properties in cylindrical cells.