While Lithium-ion batteries have the potential to serve as an excellent means of energy storage, they suffer from several operational safety concerns. Temperature excursion beyond a specified limit for a Lithium-ion battery triggers a sequence of decomposition and release, which can preclude thermal runaway events and catastrophic failure. To optimize liquid or air-based convective cooling approaches, it is important to accurately model the thermal response of Lithium-ion cells to convective cooling, particularly in high-rate discharge applications where significant heat generation is expected. This paper presents closed-form analytical solutions for the steady-state temperature profile in a convectively cooled cylindrical Lithium-ion cell. These models account for the strongly anisotropic thermal conductivity of cylindrical Lithium-ion batteries due to the spirally wound electrode assembly. Model results are in excellent agreement with experimentally measured temperature rise in a thermal test cell. Results indicate that improvements in radial thermal conductivity and axial convective heat transfer coefficient may result in significant peak temperature reduction. Battery sizing optimization using the analytical model is discussed, indicating the dependence of thermal performance of the cell on its size and aspect ratio. Results presented in this paper may aid in accurate thermal design and thermal management of Lithium-ion batteries.