Electronic systems increasingly suffer from component variation, thermal hotspots, wearout mechanisms, and other subtle physical phenomena. Systems based in FPGAs have unique opportunities for adapting to such effects. Required, however, is a low-cost, fine-grained method for sensing physical parameters. This paper describes the design of a compact multi-use sensor implemented in reconfigurable logic, and explains how to use the sensor for measuring variations in power, temperature, and wearout. We introduce enhanced procedures that solve or avoid long-standing difficulties, such as how to characterize static power variations. We implement the proposed approach in a MicroBlaze-based demonstration system that uses a Virtex-5. The system is instrumented with over 100 sensors that each fit into a single CLB, for a total sensor overhead of only 1.3%. Results from thermally-controlled hardware experiments provide some surprising insights and demonstrate the power of such on-line sensing. The method helps opens the door to better power, reliability, and health management schemes for FPGA systems.