Electronic system designs that ignore process variation are unreliable and inefficient. In this paper, we propose a system-level framework for the analysis of temperature-induced failures that considers the uncertainty due to process variation. As an intermediate step, we also develop a probabilistic technique for dynamic steady-state temperature analysis. Given an electronic system under a certain workload, our framework delivers the corresponding survival function, founded on the basis of well-established reliability models, with a closed-form stochastic parameterization in terms of the quantities that are uncertain at the design stage. The proposed solution is exemplified considering systems with periodic workloads that suffer from the thermal-cycling fatigue. The analysis of this fatigue is a challenging problem as it requires the availability of detailed temperature profiles, which are uncertain due to the variability of process parameters. To demonstrate the computational efficiency of our framework, we undertake a design-space exploration procedure to minimize the expected energy consumption under a set of timing, thermal, and reliability constraints.