Migrating threads away from the hot cores in a multicore processor allows them to operate at up to higher speeds. While this technique has already attracted a lot of research effort, the majority of thread migration studies are simulation-based. Although they are valuable for micro-architectural level optimization, they require prohibitively long simulation times, and hence have limited value for early design space exploration. We derive closed form expressions for the steady-state throughput of a multicore processor that employs thread migration and throttling for thermal management. These expressions can be evaluated under a millisecond (vs days for cycle-accurate simulation), and allow designers greater flexibility in evaluating the trade-offs involved in implementing thread migration on-chip. We also developed a system-level power/thermal simulator that we used to validate the analytical results.