The oceans of the world have a huge thermal capacity. Just like any capacitor, the oceans will have a response curve associated with changes in that thermal capacity. The shape of the charge curve does not have to be the same as the discharge curve and in fact rarely is the same. You can short a battery and it will discharge much quicker than you can charge the battery unless you have an infinite power supply in your tool box. If you happen to look at the coefficient of heat exchange between air and water, you will find that the rough "average" ratio is 100:1 water to air. It is easier to discharge heat energy stored in water to air than it is to discharge energy stored in air to water. So "charging" the world's oceans with heat stored in the atmosphere is not a quick process.
There is an inverse relationship that has to be understood between the ocean heat capacity and the Stratospheric temperatures. As the oceans collect energy, there is less energy flowing through the Stratosphere, so the temperatures in the Stratosphere would cool. When the oceans release energy, there is more energy flow through the Stratosphere, so the Stratosphere temperature would increase. Unfortunately, the resistance to energy flow in the Stratosphere can vary with composition, but still, the relationship holds well enough to be useful.
The chart above is the Stratosphere temperature anomalies for the indicated regions normalized by dividing by the standard deviation and invert to correlate with ocean heat capacity.
The two black arrows are responses to volcanic eruptions. In both cases, the oceans released energy to compensate for the impact of the volcanic aerosols. The Blue arrow is related to the 1998 El Nino. The tropical oceans lost heat to the atmosphere and the northern and southern extratropical regions gained heat, the Red arrow. Since the total heat capacity of the tropical oceans is greater than the combined extratropical oceans, there was a net loss in total ocean heat capacity.
The black curve is the approach curve of the ocean heat capacity using the Stratospheric "Wattmeter". This indicates that the rate of Ocean Heat uptake is slowing. The Stratospheric "Wattmeter" is not by any stretch of the imagination "ideal", but it can be useful.
So if your geeky friends show you a reconstruction of ocean heat uptake with some exponential rise intended to intimidate, just mention the Stratospheric "Wattmeter" to them. They will have obviously neglected this piece of information since it either goes against their agenda or they are clueless.