Safe and reliable operation of a Li-ion battery requires control and often management of the thermal envelope. In this context, a two-dimensional, transient mathematical model comprising conservation of charges, species, and energy together with electroneutrality, constitutive relations and relevant initial and boundary conditions for a spiral-wound cylindrical Li-ion battery is derived and solved numerically for passive thermal management with and without a phase change material (PCM) at various galvanostatic discharge rates. Two-way coupling of the electrochemical and thermal equations of change is attained through heat generation terms and temperature-dependent physical properties. Within this framework, the electrochemical and thermal behavior is discussed in terms of edge effects arising from the design of the spiral-wound structure and variations in heat generation in the functional layers. In addition, the cell performance with passive thermal management through a PCM is shown to lower the overall temperature of the cell at discharge rates around 5C-rates, provided the PCM layer is thick enough to provide cooling during the entire discharge. The model can be employed for wide-ranging parameter studies as well as multi-objective optimization of not only design parameters pertaining to the spirals but also, for example, for design of the thickness of the PCM layer.