Multi-Processor Systems-on-Chip (MPSoCs) are penetrating the electronics market as a powerful, yet commercially viable, solution to answer the strong and steadily growing demand for scalable and high performance systems, at limited design complexity. However, it is critical to develop dedicated system-level design methodologies for multi-core architectures that seamlessly address their thermal modeling, analysis and management. In this work, we first formulate the problem of system-level thermal modeling and link it to produce a global thermal management formulation as a discrete-time optimal control problem, which can be solved using finite-horizon model-predictive control (MPC) techniques, while adapting to the actual time-varying unbalanced MPSoC workload requirements. Finally, we compare the system-level MPC-based thermal modeling and management approaches on an industrial 8-core MPSoC design and show their different trade-offs regarding performance while respecting operating temperature bounds.