With technological advances, the number of cores integrated on a chip is increasing. This in turn is leading to thermal constraints and thermal design challenges. Temperature gradients and hotspots not only affect the performance of the system but also lead to unreliable circuit operation and affect the lifetime of the chip. Meeting temperature constraints and reducing hotspots are critical for achieving reliable and efficient operation of complex multi-core systems. In this article, we analyze the use of four of the most promising families of online control techniques for thermal management of multiprocessors system-on-chip (MPSoC). In particular, in our exploration, we aim at achieving an online smooth thermal control action that minimizes the performance loss as well as the computational and hardware overhead of embedding a thermal management system inside the MPSoC. The definition of the optimization problem to tackle in this work considers the thermal profile of the system, its evolution over time, and current time-varying workload requirements. Thus, this problem is formulated as a finite-horizon optimal control problem, and we analyze the control features of different online thermal control approaches. In addition, we implemented the policies on an MPSoC hardware simulation platform and performed experiments on a cycle-accurate model of the eight-core Niagara multi-core architecture using benchmarks ranging from Web-accessing to playing multimedia. Results show different trade-offs among the analyzed techniques regarding the thermal profile, the frequency setting, the power consumption, and the implementation complexity.