This proposal addresses the fundamental challenges in todays on-chip thermal sensing and control problems. The thermal sensing technique in even the most recent processors predominantly relies on thermal diodes or sensors. Both suffer from the fixed-location problem as on-chip hot spots migrate at run time. This project aims to develop novel techniques for spectrum and high precision temperature sensing to mitigate this problem. The proposed solutions can lead to more efficient and effective on-line thermal management. The intellectual merit of the project includes the development of a fast, lean, and accurate software thermal sensor for online temperature tracking. The software adopts a highly efficient and fine-tuned numerical method to calculate temperatures at a fine granularity both temporally and spatially. Experimentation will demonstrate its superior accuracy and speed, and hence the great potential of becoming a truly competitive remedy for chip temperature sensing.