Increasing power densities have led to the dark silicon era, for which heterogeneous multicores with different power and performance characteristics are promising architectures. This paper focuses on maximizing the overall system performance under a critical temperature constraint for heterogeneous tiledmulticores, where all cores or accelerators inside a tile share the same voltage and frequency levels. For such architectures, we present a resourcemanagement technique that introduces power density as a novel system level constraint, in order to avoid thermal violations. The proposed technique then assigns applications to tiles by choosing their degree of parallelism and the voltage/frequency levels of each tile, such that the power density constraint is satisfied. Moreover, our technique provides runtime adaptation of the power density constraint according to the characteristics of the executed applications, and reacting to workload changes at runtime. Thus, the available thermal headroom is exploited to maximize the overall system performance.