White dwarfs (WDs) are the final evolutionary product of the vast majority of stars in the Universe. They are electron-degenerate structures characterized by no stable thermonuclear activity, and their evolution is generally described as a pure cooling process. Their cooling rate is adopted as cosmic chronometer to constrain the age of several Galactic populations, including the disk, globular and open clusters. By analysing high-resolution photometric data of two very similar Galactic globular clusters (M3 and M13), we find a clear-cut and unexpected overabundance of bright WDs in M13. Theoretical models suggest that, consistent with the horizontal branch morphology, this overabundance is due to a slowing down of the cooling process in ~70% of the WDs in M13, caused by stable thermonuclear burning in their residual hydrogen-rich envelope. The presented observational evidence of quiescent thermonuclear activity occurring in cooling WDs brings new attention on the use of the WD cooling rate as cosmic chronometer for low-metallicity environments.