In this paper, we present two approaches to improve the execution of OpenMP applications on the IBM Cyclops multithreaded architecture. Both solutions are independent and they are focused to obtain better performance through a better management of the cache locality. The first solution is based on software modifications to the OpenMP runtime library to balance stack accesses across all data caches. The second solution is a small hardware modification to change the data cache mapping behavior, with the same goal. Both solutions help parallel applications to improve scalability and obtain better performance in this kind of architectures. In fact, they could also be applied to future multi-core processors. We have executed (using simulation) some of the NAS benchmarks to prove these proposals. They show how, with small changes in both the software and the hardware, we achieve very good scalability in parallel applications. Our results also show that standard execution environments oriented to multiprocessor architectures can be easily adapted to exploit multithreaded processors.