In experiments with CO2 concentration increasing at 1% per year in atmosphere--ocean general circulation models (AOGCMs), the rate of global ocean heat uptake N (W m-2) and the global-mean surface temperature change T both increase with time. Their ratio N/T at the time of 2xCO2, called the ocean heat uptake efficiency (OHUE, W m-2 K-1), has a large spread across AOGCMs, and correlates highly with the strength of the Atlantic meridional overturning circulation (AMOC) in the unperturbed climates of the models. Models with stronger AMOC have smaller T at the time of 2xCO2, smaller warming in the upper few 100 m, and larger warming below. However, the time-integrated ocean heat uptake (OHU, J) at the time of 2xCO2 does not correlate significantly with AMOC or OHUE. That is, greater OHUE does not mean more heat is taken up. Instead, it means that heat is transferred more effectively from  the surface to the deeper ocean, so that T is smaller, and OHUE=N/T is larger. Heat is taken up by the ocean mostly as a passive tracer, by the wind-driven overturning and eddy-induced transports. The spread of OHUE among models and its correlation with AMOC are related to the unperturbed state of the ocean, not to any effect of climate change. In particular, weaker eddy-induced transports give weaker stratification, deeper warming, greater OHU and stronger AMOC. On the basis of these results and ideas, we propose a modified conceptual model of the Earth energy balance.