On-chip thermal management is quintessential to a thermally safe operation of a many-core processor. The presence of a physically distributed logically shared Last-Level Cache (LLC) significantly reduces the performance penalty of migrating threads within the cores of an S-NUCA many-core. This cost reduction allows novel thermal management of these many-cores via synchronous thread migration. Synchronous thread migration provides a viable alternative to Dynamic Voltage and Frequency Scaling (DVFS) and asynchronous thread migration used traditionally to manage thermals of S-NUCA many-cores. We present a theoretical method to compute the peak tem-perature in many-cores with synchronous thread migrations. We use the method to create a thermal management heuristic called HotPotato that maximizes the performance of S-NUCA many-cores under a peak temperature constraint. We implement HotPotato within the state-of-the-art HotSniper simulator. Detailed interval thermal simulations with HotSniper show an average 10.72% improvement in response time of S-NUCA many-cores when scheduling with HotPotato compared to a state-of-the-art thermal-aware S-NUCA scheduler.