Although manycore processors have plenty of cores, not all of them may run simultaneously at full speed and even some of them might need to be power-gated in order to keep the chip within safe temperature limits. Hence, a resource management technique, that allocates cores to application aiming at maximizing the system performance, will not be able to achieve its goal without taking into account the on-chip temperature and its impact on the availability of the chip's resources. However, considering a temperature constraint by the resource management will further increase its complexity, especially in manycores, and thus implementing it in a centralized scheme might lead to a computation bottleneck and a single point of failure. To avoid such scenarios, it is inevitable to distribute the computation required by the resource management technique throughout the chip. In this article, we propose a distributed resource management technique that considers temperature as an essential factor in allocating cores to applications and determining the power states of these cores and their voltage/frequency levels, while taking into account the performance models of the applications in order to maximize the overall system performance under a temperature constraint. Our proposed technique employs, for the first time, combinatorial auctions within an agent system to achieve the targeted goal in a distributed manner. The experimental evaluations show that our proposed technique achieves significant performance improvements with an average of 41% compared to several distributed resource management techniques.