A novel type of superconducting transition edge sensor is proposed. In this sensor, the temperature of a superconducting film is held constant by feeding back to its position on the resistive transition edge. Energy deposited in the film is measured by a reduction in the feedback Joule heating. This mode of operation should lead to substantial improvements in resolution, linearity, dynamic range, and count rate. Fundamental resolution limits are below ΔE=√kT2C, which is sometimes incorrectly referred to as the thermodynamic limit. This performance is better than any existing technology operating at the same temperature, count rate, and absorber heat capacity. Applications include high resolution x‐ray spectrometry, dark matter searches, and neutrino detection. © 1995 American Institute of Physics.