<jats:p>Abstract. The surface mass balance scheme dEBM (diurnal Energy Balance Model) provides a novel interface between the atmosphere and land ice for Earth system modeling, which is based on the energy balance of glaciated surfaces. In contrast to empirical schemes, dEBM accounts for changes in the Earth’s orbit and atmospheric composition. The scheme only requires monthly atmospheric forcing (precipitation, temperature, shortwave and longwave radiation, and cloud cover). It is also computationally inexpensive, which makes it particularly suitable to investigate the ice sheets' response to long-term climate change. After calibration and validation, we analyze the surface mass balance of the Greenland Ice Sheet (GrIS) based on climate simulations representing two warm climate states: a simulation of the mid-Holocene (approximately 6000 years before present) and a climate projection based on an extreme emission scenario which extends to the year 2100. The former period features an intensified summer insolation while the 21st century is characterized by reduced outgoing longwave radiation. Specifically, we investigate whether the temperature–melt relationship, as used in empirical temperature-index methods, remains stable under changing insolation and atmospheric composition. Our results indicate that the temperature–melt relation is sensitive to changes in insolation on orbital timescales but remains mostly invariant under the projected warming climate of the 21st century. </jats:p>