Due to an imbalance between incoming and outgoing radiation at the top of the atmosphere, excess heat has accumulated in Earth's climate system in recent decades, driving global warming and climatic changes. To date, it has not been quantified how much of this excess heat is used to melt ground ice in permafrost. Here, we diagnose changes in sensible and latent ground heat contents in the northern terrestrial permafrost region from ensemble-simulations of a tailored land surface model. We find that between 1980 and 2018, about 3.9 (+1.4/-1.6) ZJ of heat, of which 1.7 (+1.3/-1.4) ZJ (44%) were used to melt ground ice, were absorbed by permafrost. Our estimate, which does not yet account for the potentially increased heat uptake due to thermokarst processes in ice-rich terrain, suggests that permafrost is a persistent heat sink comparable in magnitude to other components of the cryosphere and must be explicitly considered when assessing Earth's energy imbalance.