The deep-ocean heat uptake (DOHU) in transient climate changes is studied using an ocean general circulation model (OGCM) and its adjoint. The model configuration consists of idealized Pacific and Atlantic basins. The model is forced with the anomalies of surface heat and freshwater fluxes from a global warming scenario with a coupled model using the same ocean configuration. In the scenario CO2 concentration increases 1% per year. The heat uptake calculated from the coupled model and from the adjoint are virtually identical, showing that the heat uptake by the OGCM is a linear process. After 70 years the ocean heat uptake is almost evenly distributed within the layers above 200 m, between 200 and 700 m, and below 700 m (about 20 x 10²² J in each). The effect of anomalous surface fresh water flux on the DOHU is negligible. Analysis of CMIP-2 data for the same global warming scenario shows that qualitatively similar results apply to coupled atmosphere-ocean GCMs. The penetration of surface heat flux to the deep ocean in our OGCM occurs mainly in the North Atlantic and the Southern Ocean, since both the sensitivity of DOHU to the surface heat flux and the magnitude of anomalous surface heat flux are large in these two regions. The DOHU relies on the reduction of convection and Gent-McWilliams-Redi mixing in the North Atlantic, and the reduction of Gent-McWilliams- Redi mixing in the Southern Ocean.