Skill in decadal climate prediction is usually assessed statistically, yet the physical origin of the added value from initialization remains unclear. Here we show that residual prediction skill in near-surface air temperature, after removal of the externally forced response, can be traced through a surface energy-budget framework. Using CESM-DPLE initialized predictions, CESM-LE uninitialized simulations and observations, we decompose residual SAT variability into radiative, heat-storage and turbulent-flux contributions. At the 1-year lead, residual skill is concentrated over the tropical Pacific and is partly associated with ENSO-related cloud-radiative and air–sea coupling anomalies. At multi-year leads, the dominant signal shifts to extratropical ocean-memory regions, especially the subpolar North Atlantic and Southern Ocean, with related skill extending to adjacent land areas. In these regions, heat-storage anomalies identify the oceanic reservoir of predictability, while turbulent heat fluxes regulate the release of stored ocean heat to the lower atmosphere. Clear-sky downward longwave radiation provides the most spatially coherent positive contribution, indicating that ocean memory influences SAT not only through local surface exchange, but also through lower-tropospheric warming, moistening and radiative adjustment. These results show that initialization-related decadal temperature predictability is shaped by a coupled pathway linking ocean heat storage, air–sea turbulent exchange and atmospheric longwave radiative feedback.