The ultraviolet emission from the solar transition region is dominated by dynamic, low-lying magnetic loops. The enhanced spatial and temporal resolution of the solar observation satellite Interface Region Imaging Spectrograph (IRIS) has made it possible to study these structures in fine detail. IRIS has observed ‘transient brightenings’ in these loops, associated with strong excess line broadenings1,2 providing important clues to the mechanisms that heat the solar atmosphere. However, the physical origin of the brightenings is debated. The line broadenings have been variously interpreted as signatures of nanoflares3, magneto-hydrodynamic turbulence4, plasmoid instabilities5 and magneto-acoustic shocks6. Here we use IRIS slit-jaw images and spectral data, and the Atmospheric Imaging Assembly of the Solar Dynamics Observatory spacecraft, to show that the brightenings are consistent with magnetic-reconnection-mediated impulsive heating at field-line braiding sites in multi-stranded transition-region loops. The spectroscopic observations present evidence for preferential heating of heavy ions from the transition region and we show that this is consistent with ion cyclotron turbulence caused by strong currents at the reconnection sites. Time-dependent differential emission measure distributions are used to determine the heating frequency7,8,9 and to identify pockets of faintly emitting ‘super-hot’ plasma. The observations we present and the techniques we demonstrate open up a new avenue of diagnostics for reconnection-mediated energy release in solar plasma.