The safe and effective operation of Li-ion batteries requires Advanced Battery Management Systems (ABMSs), which can be designed by Model Predictive Control (MPC). The dynamics of Li-ion batteries are well described by a set of highly nonlinear and tightly coupled partial differential algebraic equations that arise from porous electrode theory, but the expressions are too complex to be included in the real-time optimization calculations carried out by MPC. For this reason, a linearized version of such models has been used in past studies. Such linear models do not describe all of the important dynamic nonlinearities of Li-ion battery operations, especially with regard to thermal management, and such plant-model mismatch can degrade performance and lead to violation of operational constraints. This paper proposes a Hybrid MPC (HMPC) algorithm that incorporates a PieceWise Affine AutoRegressive eXogenous (PWARX) battery model constructed using a tailored clustering and identification algorithm. Simulations show that this model better approximates the thermal behavior of the Li-ion cell, and obtains better closed-loop performance when compared to MPC based on an ARX model.