Characterization of rock discontinuities and rock bridges is required to define stability conditions of fractured rock masses in both natural and engineered environments. Although remote sensing methods for mapping discontinuities have improved in recent years, remote detection of intact rock bridges on cliff faces remains challenging, with their existence typically confirmed only after failure. In steep exfoliating cliffs, such as El Capitan in Yosemite Valley (California, USA), rockfalls mainly occur along cliff-parallel exfoliation joints, with rock bridges playing a key role in the stability of partially detached exfoliation sheets. We employed infrared thermal imaging (i.e., thermography) as a new means of detecting intact rock bridges prior to failure. An infrared thermal panorama of El Capitan revealed cold thermal signatures for the surfaces of two granitic exfoliation sheets, consistent with the expectation that air circulation cools the back of the partially detached sheets. However, we also noted small areas of warm thermal anomalies on these same sheets, even during periods of nocturnal rock cooling. Rock attachment via rock bridges is the likely cause for the warm anomalies in the thermal data. 2-D model simulations of the thermal behavior of one of  the monitored sheets reproduce the observed anomalies and explain the temperature differences detected in the rock bridge area. Based on combined thermal and ground-based lidar imaging, and using geometric and rock fracture mechanics analysis, we are able to quantify the stability of both sheets. Our analysis demonstrates that thermography can remotely detect intact rock bridges and thereby greatly improve rockfall hazard assessment.