While Li-ion cells offer excellent electrochemical performance for several applications including electric vehicles, they also exhibit poor thermal transport characteristics, resulting in reduced performance, overheating and thermal runaway. Inadequate heat removal from Li-ion cells originates from poor thermal conductivity within the cell. This paper identifies the rate-limiting material-level process that dominates overall thermal conduction in a Li-ion cell. Results indicate that thermal characteristics of a Li-ion cell are largely dominated by heat transfer across the cathode-separator interface rather than heat transfer through the materials themselves. This interfacial thermal resistance contributes around 88% of total thermal resistance in the cell. Measured value of interfacial resistance is close to that obtained from theoretical models that account for weak adhesion and large acoustic mismatch between cathode and separator. Further, to address this problem, an amine-based chemical bridging of the interface is carried out. This is shown to result in in four-times lower interfacial thermal resistance without deterioration in electrochemical performance, thereby increasing effective thermal conductivity by three-fold. This improvement is expected to reduce peak temperature rise during operation by 60%. By identifying and addressing the material-level root cause of poor thermal transport in Li-ion cells, this work may contributes towards improved thermal performance of Li-ion cells.