The increasing usage of multi-cores in safety-critical applications, such as autonomous control, demands high levels of reliability, which crucially depends on the temperature. On the other hand, there is a natural trade-off between reliability and performance. The scheduling of tasks is one of the key factors which determine the resulting system performance as well as reliability. Commonly used techniques, such as simulation based on benchmarks, can simulate only a limited number of input sequences of system runs and hardly optimize the performance-reliability trade-off. In order to accurately evaluate the schedulers and provide formal guarantees suitable in early design stages, we use formal methods for a quantitative performance-reliability trade-off analysis. Specifically, we propose to use energy-utility quantiles as a metric to evaluate the effectiveness of a given scheduler. For illustration, we evaluate TAPE, a state-of-the-art thermal-constrained scheduler, with theoretical optimal ones.