Real-time estimation of battery internal states and physical parameters is of the utmost importance for intelligent battery management systems (BMS). Electrochemical models, derived from the principles of electrochemistry, are arguably more accurate in capturing the physical mechanism of the battery cells than their counterpart data-driven or equivalent circuit models (ECM). Moreover, the electrochemical phenomena inside the battery cells are coupled with the thermal dynamics of the cells. Therefore, consideration of the coupling between electrochemical and thermal dynamics inside the battery cell can be potentially advantageous for improving the accuracy of the estimation. In this paper, a nonlinear adaptive observer scheme is developed based on a coupled electrochemical–thermal model of a Li-ion battery cell. The proposed adaptive observer scheme estimates the distributed Li-ion concentration and temperature states inside the electrode, and some of the electrochemical model parameters, simultaneously. These states and parameters determine the state of charge (SOC) and state of health (SOH) of the battery cell. The adaptive scheme is split into two separate but coupled observers, which simplifies the design and gain tuning procedures. The design relies on a Lyapunov's stability analysis of the observers, which guarantees the convergence of the combined state-parameter estimates. To validate the effectiveness of the scheme, both simulation and experimental studies are performed. The results show that the adaptive scheme is able to estimate the desired variables with reasonable accuracy. Finally, some scenarios are described where the performance of the scheme degrades.