In the atmosphere there's a situation: The weather all happens down near the surface, in a region called the troposphere. Here the density/temperature gradients can result in instabilities, where a parcel of air that is, say, lighter than its sourroundings can become MORE ligher-than-its surroundings as it moves up (and vice-versa). Above that is another (set of) layer(s) called the "stratosphere", where everything is most stable right where it is. Nothing very exciting happens there except when something coming up REALLY fast from below coasts up a bit before it stabilizes and moves back down.
The oceans do something similar, but upside down:
Water has an interesting property: Like most materials it gets more dense as it gtss colder - but only up to a point. As it approaches freezing the molecules start hanging out in larger groups, working their way toward being ice crystals. The hydrogens on one molecule attract the oxygens on another, and because of the angle between the hydrogens bondended to the oxygen in each molecule, the complexes are somewhat LESS dense than liquid. As a result, with progressively lower temperatures the density reaches a maximum, then the water begins to expand again. When it actually freezes it is so much less dense than near-freezing liquid that the ice floats. With fresh water the maximum density happens about 4 degrees C. Salt disrupts the crystalization somewhat so the maximum density is a tad cooler (and varies a bit with salt concentration - and thus depth), but the behavior is similar.
The result is that, when you have a mix of cooler and hotter blobs of fresh water, the water closer to 4 degrees sinks and that farther from it rises. The result is that, absent a heat or impurity source below, the bottom (and much of the volume) of a deep lake tends to be stable, stratified, water at about 4 degrees year around, while all the deviations from it and "weather" activity is in no more than about the top 300 feet: Wave action, ice, hot and cold currents, etc. are all above the reasonably abrupt "thermocline" boundary. Below that things are very slow, driven mostly by things like volcanic heat. (Diffusion is REALLY slow in calm water. It takes decades for, say, dissolved impurities to move a couple inches.)
The ocean is much like that, too, but a little cooler and with some temperature ramps spreading out the thermocline due to variations in salt concentration.
So global warming/cooling/weather, whatever would NOT be expected to affect deep water temperatures. This would all be happening in the top few hundred feet. If, say, the ocean were heating up without the surface water temperature changing, this would take the form of the thermocline gradually lowering near the equator and/or rising near the poles, rather than the deep water becoming warmer.