It seems like that might be the case but actually, it is not true. There’s a lot of thermodynamic properties involved but in reality, the faster moving coolant removes the same number of BTUs- up to a point. The greater the differential in temperature, the greater the potential for heat transfer. Heat transfer slows as the two elements approach the same temperature. So more dwell time is usually not more efficient. Bear in mind, molecules with less heat are constantly replacing those that have left the scene to dump their energy and return again. A properly designed thermal regulation system (see, not a coolant) can dump heat faster than it can be generated. The radiator is more efficient at losing heat than the engine is at generating it. That’s why the thermostat opens and closes during normal operation. It is regulating the engine temperature.
The analogy doesn’t hold because your finger is leaving the hot water and cooling during that period. Leave your finger in the hot water and see if swishing it faster feels cooler than leaving it still 
All this typing- it’s a complicated topic. I went looking and lo and behold, found someone already explained it better than I could 
Myths
For those that cling tenaciously to myths, I am going to take one last crack at forever dispelling the Granddaddy of them all when it comes to cooling systems.
The myth is stated as either:
- Coolant can be pumped too fast through the engine for it to absorb enough heat, or
- Coolant can be pumped too fast through the radiator for it to cool properly, or
- Cooling can be improved by slowing the flow of coolant through the radiator so it cools more completely.
NONE of these is true. The simple truth is that higher coolant flow will ALWAYS result in higher heat transfer and improved cooling system performance.
The reason the myth is so persistent, is that: a) without knowledge of fluid dynamics and laws of thermal conduction it does make a kind of intuitive sense and b) it is based on a tiny kernel of truth, but that kernel of truth does not explain the overall system behaviour and so, interpreted out of context, leads to a completely erroneous conclusion.
So, let’s start with the tiny nugget of truth. If you had a sealed rad (no flow) full of hot coolant, and subjected that rad to airflow, yes, the longer you left the coolant in the rad, the more it would cool. However, if you were to plot that cooling over time, you would find that the RATE at which the cooling takes place is an exponential curve that decreases with the temperature difference between the hot coolant and the air. Put another way - when the temperature difference (delta-T) between the hot coolant and the airflow is large, heat transfer (cooling) initially takes place very, very quickly (almost instantaneously). But as that happens, and the coolant cools, the delta-T becomes less, and the RATE at which further cooling happens gets less and less until the point where the coolant and air are almost the same temperature and continued cooling takes a very long time. This is Newton’s law of cooling. To illustrate this, recall my “quenching steel in a bucket” analogy.
A good example of this law can be seen when quenching a red-hot piece of steel in a bucket of water. At first, the temperature difference (delta-T) between the red-hot steel and the water is huge - therefore the initial heat transfer occurs at a great rate - the steel initially cools very fast - almost instantaneously. However, after this initial cooling, the delta-T is much smaller, so the remaining cooling occurs much more slowly. If you removed the steel after a second or two - it has cooled a lot - but it will still be warm. To continue cooling the steel to the temp. of the water, you have to leave it in there quite a bit longer - because as it cools - the rate of cooling continually decreases as well. In short - initial cooling is fast, but subsequent cooling occurs more and more slowly until cooling that last little bit takes a long time.
So what does this mean? Basically it means, the longer the coolant stays in the rad, the less efficient the cooling that takes place is - to the point that the rate of cooling is so slow as to be detrimental to overall system cooling . Better to dump the big load of heat right away and go back quickly for another load than hang about waiting for a last little bit of insignificant cooling to happen.
