The temperature of deep water is around 3 or 4°C. However, in the Earth's crust, temperature increases with depth (e.g., 66°C in some underground mine). So, why would the water be cold?
If the heat is generated by the soil itself (say, radioactive potassium or whatever), even if such heating would not occur in water, one could expect it to happen in the soil just below the water, thus warming it but this does not happen (except for submarine volcanic activity but this is different).
Soil/rock is fixed in place (for human timescales). Heat transfer takes place through conduction only at this timescale. The surface of the earth is in thermal equilibrium at a few hundred K, while the core of the earth is several thousand K. This means there must be a temperature gradient as we descend.
The ocean is a fluid and can move heat by convection. Any large temperature gradient causes flows that rapidly move the heat away. Thermal energy does transfer from the bottom of the ocean into the water, but the water moves in response, replacing it with cooler water.
You can take the example of a pot full of water which is kept on gas stove ( given in the figure)
!(https://i.sstatic.net/x33Qi.jpg)
You can see that the bottom part of the pot is being heated continuously and the heat is transferred to the liquid since liquid is in contact with that part. You can see that this phenomenon is termed as Convection since the particles which carry the energy move freely and transfer the heat. The hotter liquid moves away from the bottom region (since they are free to do so) and colder liquid from its surrounding takes the position and this process is continuous .
In case of oceans the same process occurs . If they get enough energy some molecules escape the surface which we call evaporation. So all in all its the moving characteristics of water that keeps it cool at the bottom.
Perhaps the density as a function of temperature has a large effect. It is highest a few degrees above freezing. Lakes 'turnover' abruptly as winter approaches when the bottom layer of warm water comes up and the cooler water descends. A continuous process of redistribution would be likely in the oceans.
Doesn't it have to do with the fact that deep water is almost entirely untouched by sunlight and thus solar radiation in the form of UV and visible photons, while deep soil is more easily permeated by such radiation (also as you go deeper in the soil you get closer to the earth's core relatively?). That would be my guess, but I am probably wrong, and if I'm not I am probably ill equipped to add nuance to this topic.
