The need to develop systems that exploit multi and many-core architectures to reduce wasteful heat generation is of utmost importance in compute-intensive applications. We propose an energy-conscious approach to multicore scheduling known as non-preemptive dynamic window (NPDW) scheduling that achieves effective load and temperature balancing over chip multiprocessors. NPDW utilizes the concept of dynamic time windows to accumulate tasks and find an optimal stable matching between accumulated tasks and available processor cores using a modified Gale-Shapely algorithm. The metrics of window and matching performance are defined to create a dynamic window heuristic to determine the next time window size based on the current and previous window sizes. Based on derived formulation and experimental results, we show that our NPDW scheduler is able to distribute the computational and thermal load throughout the processors in a multicore environment better than baseline schedulers. We believe that within multicore compute applications requiring temperature and energy-conscious system design, our scheduler may be employed to effectively disperse system load and prevent excess core heating.