The emergence of multicore and manycore processors is set to change the parallel computing world. Applications are shifting towards increased parallelism in order to utilise these architectures efficiently. This leads to a situation where every application creates its desirable number of threads, based on its parallel nature and the system resources allowance. Task scheduling in such a multithreaded multiprogramming environment is a significant challenge. In task scheduling, not only the order of the execution, but also the mapping of threads to the execution resources is of a great importance. In this paper we state and discuss some fundamental rules based on results obtained from selected applications of the BOTS benchmarks on the 64-core TILEPro64 processor. We demonstrate how previously efficient mapping policies such as those of the SMP Linux scheduler become inefficient when the number of threads and cores grows. We propose a novel, low-overhead technique, a heuristic based on the amount of time spent by each CPU doing some useful work, to fairly distribute the workloads amongst the cores in a multiprogramming environment. Our novel approach could be implemented as a pragma similar to those in the new task-based OpenMP versions, or can be incorporated as a distributed thread mapping mechanism in future manycore programming frameworks. We show that our thread mapping scheme can outperform the native GNU/Linux thread scheduler in both single-programming and multiprogramming environments.