Sunspot light bridges (LBs) exhibit a wide range of short-lived phenomena in the chromosphere and transition region. In contrast, we use here data from the Multi-Application Solar Telescope (MAST), the Interface Region Imaging Spectrograph (IRIS), Hinode, the Atmospheric Imaging Assembly (AIA), and the Helioseismic and Magnetic Imager (HMI) to analyze the sustained heating over days in an LB in a regular sunspot. Chromospheric temperatures were retrieved from the MAST Ca ii and IRIS Mg ii lines by nonlocal thermodynamic equilibrium inversions. Line widths, Doppler shifts, and intensities were derived from the IRIS lines using Gaussian fits. Coronal temperatures were estimated through the differential emission measure, while the coronal magnetic field was obtained from an extrapolation of the HMI vector field. At the photosphere, the LB exhibits a granular morphology with field strengths of about 400 G and no significant electric currents. The sunspot does not fragment, and the LB remains stable for several days. The chromospheric temperature, IRIS line intensities and widths, and AIA 171 and 211 Å intensities are all enhanced in the LB with temperatures from 8000 K to 2.5 MK. Photospheric plasma motions remain small, while the chromosphere and transition region indicate predominantly redshifts of 5–20 km s−1 with occasional supersonic downflows exceeding 100 km s−1. The excess thermal energy over the LB is about 3.2 × 1026 erg and matches the radiative losses. It could be supplied by magnetic flux loss of the sunspot (7.5 × 1027 erg), kinetic energy from the increase in the LB width (4 × 1028 erg), or freefall of mass along the coronal loops (6.3 × 1026 erg).