We present a thermal-aware, hard real-time (HRT) global scheduler for a multiprocessor system designed upon three novel techinques. First, we present a modeling methodology based on Timed Continuous Petri nets (TCPN) that yields a complete state variable model, including job arrivals, CPU usage, power, and thermal behavior. The model is accurate and avoids the calibration stage of RC thermal models. Second, based on this model, a linear programming problem (LPP) determines the existence of a feasible HRT thermal-aware schedule. Last, a sliding-mode controller and an online discretization algorithm implement the global HRT scheduler, which is capable of managing thermal constraints, context switching, migrations, and disturbances.