The 2015 Paris Agreement proposed targets to limit global-mean surface temperature (GMST) rise well below 2°C relative to preindustrial level by 2100, requiring a cease in the radiative forcing (RF) increase in the near future. In response to changing RF, the deep ocean responds slowly (ocean slow response), in contrast to the fast ocean mixed layer adjustment. The role of the ocean slow response under low warming targets is investigated using representative concentration pathway (RCP) 2.6 simulations from phase 5 of the Coupled Model Intercomparison Project. In RCP2.6, the deep ocean continues to warm while RF decreases after reaching a peak. The deep ocean warming helps to shape the trajectories of GMST and fuels persistent thermosteric sea level rise. A diagnostic method is used to decompose further changes after the RF peak into a slow warming component under constant peak RF and a cooling component due to the decreasing RF. Specifically, the slow warming component amounts to 0.2°C (0.6°C) by 2100 (2300), raising the hurdle for achieving the low warming targets. When RF declines, the deep ocean warming takes place in all basins but is the most pronounced in the Southern Ocean and Atlantic Ocean where surface heat uptake is the largest. The climatology and change of meridional overturning circulation are both important for the deep ocean warming. To keep the GMST rise at a low level, substantial decrease in RF is required to offset the warming effect from the ocean slow response.