As the number of transistors on a chip doubles with every technology generation, the number of on-chip cores also increases rapidly, making possible in a foreseeable future to design processors featuring hundreds of general-purpose cores. However, though a large number of cores speeds up parallel code sections, Amdahl's law requires speeding up sequential sections too. We argue that it will become possible to dedicate a substantial fraction of the chip area and power budget to achieve high sequential performance. Current general-purpose processors contain a handful of cores designed to be continuously active and run in parallel. This leads to power and thermal constraints that limit the core's performance. We propose removing these constraints with a {\it sequential accelerator} ({\bf SACC}). A SACC consists of several cores {\it designed} for ultimate sequential performance. These cores cannot run continuously. A single core is active at any time, the rest of the cores are inactive and power-gated. We migrate the execution periodically to another core to spread heat generation uniformly over the whole SACC area, thus addressing the temperature issue. The SACC will be viable only if it yields significant sequential performance. Migration-induced cache misses may limit performance gains. We propose some solutions to mitigate this problem. We also investigate a migration method using thermal sensors, such that the migration interval depends on the ambient temperature and the migration penalty is negligible under normal thermal conditions.