To better understand recent changes of Arctic sea ice thickness and extent, it is important to distinguish between the contributions of winter growth and summer melt to the sea ice mass balance. In this study we present a Lagrangian approach to quantify summer sea ice melt in which multiyear ice (MYI) floes that were surveyed by airborne electromagnetic thickness sounding within Nares Strait during summer were backtracked, using satellite imagery, to a region in close proximity (3–20 km) to spring ice thickness surveys carried out in the Lincoln Sea. Typical modal total MYI thicknesses, including ~0.4‐m snow, ranged between 3.9 and 4.7 m in the Lincoln Sea during April. Ice‐only modal thicknesses were between 2.2 and 3.0 m in Nares Strait during August. Total thinning including snow and ice was 1.3 ± 0.1 m including 0.4 ± 0.09 m of snow melt and 0.9 ± 0.2 m of ice melt. This translates to a seasonal net heat input of 305 ± 69 MJ/m^2 (262 ± 60 MJ/m^2 for ice only) and seasonal net heat flux of 57 ± 13 W/m^2 (45 ± 10 W/m^2 for ice only), which is unlikely to be explained by solar radiation fluxes alone. Furthermore, our approach provides an improvement on traditional ice mass balance buoy estimates because it integrates melt over larger spatial scales, where melt can be highly variable due to differential melt experienced between melt ponds, bare ice, hummocks, and ridges.