Heterogeneity in general-purpose workloads often end up in non optimal per-thread hardware resource usage. The current trend towards multicore architectures, containing several multithreaded cores, increases the need of a complexity-effective way to expose the heterogeneity in general-purpose workloads to the underlying hardware, in order to obtain all the potential performance of these architectures. In this paper we present the Heterogeneity-Aware Dynamic Thread Migrator (hDTM), a novel complexity-effective hardware mechanism that exposes the heterogeneity in software to the hardware, also enabling the hardware to react to the dynamic behavior variations in the running applications. By means of core-to-core thread migrations, the hDTM mechanism strives to perform the desired behavior transparently to the Operating System. As an example of the general-purpose hDTM concept presented in this paper, we describe a naive hDTM implementation for a Power5-like processor and provide results on the benefits of the proposed mechanism. Our results indicate that even this simple hDTM implementation is able to get close to hDTM’s goal, not only avoiding losses due to bad thread-to-core assignments (up to a 25%) but also going beyond the best static thread-to-core assignment upper limit.