Elevated chip temperatures are true limiters to the scalability of computing systems. Excessive runtime thermal variations compromise the performance and reliability of integrated circuits. To address these thermal issues, state-of-the-art chips have integrated thermal sensors that monitor temperatures at a few selected die locations. These temperature measurements are then used by thermal management techniques to appropriately manage chip performance. Thermal sensors and their support circuitry incur design overheads, die area, and manufacturing costs. In this paper, we propose a new direction for full thermal characterization of integrated circuits based on spectral Fourier analysis techniques. Application of these techniques to temperature sensing is based on the observation that die temperature is simply a space-varying signal, and that space-varying signals are treated identically to time-varying signals in signal analysis. We utilize Nyquist-Shannon sampling theory to devise met...