Derived from the Pseudo Two-Dimensional mathematical structure, a simplified electrochemical and thermal model of LiFePO4-graphite based Li-ion batteries is developed in this paper. Embedding the porous electrode theory, this model integrates the main design parameters of Li-ion systems and its partial differential equations mathematical structure makes it a promising candidate for battery management system (BMS) applications and comprehensive aging investigations. Based on a modified Single-Particle approach, the model is used to simulate and discuss capacity restitution in galvanostatic charges and discharges at various rates and temperatures. Constant high-rate solicitations similar to fast charge of plug-in electric vehicles or electric vehicles, are experimentally tested and simulated with the present model. Also, thermal issues occurring during these specific operating conditions are quantitatively pointed out. The concept of current-dependent spherical particle radius is used to obtain good agreement with experimental data related to galvanostatic charges and discharges. The capabilities and limits of this preliminary modeling work are discussed in detail and ways to extend the potentialities of this approach to BMS applications are proposed.