With a rapidly growing number of functions in embedded real-time systems, it becomes inevitable to integrate tasks of different safety integrity levels (SILs) into one mixed-criticality system. Here, it is important to not only isolate shared architectural resources, as tasks executing on different cores may also interfere via the processor's thermal manager. In order to prevent a scenario where best-effort tasks cause deadline violations for critical tasks, we propose a thermal management strategy that guarantees a sufficient thermal isolation between tasks of different SILs, and simultaneously reduces the run-time of best-effort tasks by up to 45 % compared to the state of the art without incurring any real-time violations for critical tasks.