Although process technology trends predict that transistor sizes will continue to shrink for a few more generations, voltage scaling has stalled and thus future chips are projected to be increasingly more power hungry than previous generations. Particularly in mobile devices which are severely cooling constrained, it is estimated that the peak operation of a future chip could generate heat ten times faster than than the device can sustainably vent. However, many mobile applications do not demand sustained performance; rather they comprise short bursts of computation in response to sporadic user activity. To improve responsiveness for such applications, this dissertation proposes computational sprinting, in which a system greatly exceeds sustainable power margins (by up to 10x) to provide up to a few seconds of high-performance computation when a user interacts with the device. Computational sprinting exploits the material property of thermal capacitance to temporarily store the excess heat generated when sprinting. After sprinting, the chip returns to sustainable power levels and dissipates the stored heat when the system is idle. This dissertation: (i) broadly analyzes thermal, electrical, hardware, and software considerations to analyze the feasibility of engineering a system which can provide the responsiveness of a plat- form with 10x higher sustainable power within today's cooling constraints, (ii) leverages existing sources of thermal capacitance to demonstrate sprinting on a real system today, and (iii) identifies the energy-performance characteristics of sprinting operation to determine runtime sprint pacing policies.