Roger the scales are not comparable. The bottom bucket is about 300 times larger than the top bucket. The top bucket is constantly deriving new energy from the sun. The bottom is constantly being cooled by melt water flowing back towards the equator from the poles, which in turn is replenished with fresh ice every winter.
First the problem of global warming is a problem of ocean surface heat. With OTEC you convert a small portion of this heat to energy and this is the only energy source that accomplishes this. Second you move a bunch more of that heat which is largely the consequence of greenhouse forcing to the depths. This in turn is what has brought about the hiatus of the past fifteen years, which now appears to be ending as the heat that was sequestered in the Western Pacific - only to a depth of about 250 meters - appears to be returning. Most dramatically off Vancouver Isand - my home - where the seasonal temperature anomally of the past 3 months is close to 4C above normal.
Convection also dictates heat in the depths will not stay there. Levitus points out to a depth of 2000 meters the oceans have only warmed .09C over the 55 year period 1955-2010. Since I am only talking about moving heat half that deep double that to say .2C. The water at a depth of 1000 meters is about 4C so now you have brought it up to 4.2C and this heat would then be expected to rise a hundred meters or so to where the ambiant temperature is 4.2C. At 1000 meters the temperature should remain pretty close to 4C.
A rise of .2C in 50 years would also mean you have closer to 250 years before you have increased the 0-1000 level by 1 C which even then would leave you a sufficient delta T in the tropics to continue producing power.
It is estimated that heat from the depths, absent any other forces, rises about 4 meters a year so in 250 years the heat you sink today will be availabe again to produce more power 250 years from now and you will probably want to sink it again then even if you no longer have a problem with CO2 in the atmosphere as a consequence of OTEC and other zero emission energy sources. Levitus states if that .09C was instantly added to the lower 10 kilometers of the atmosphere it would rise on average 36C so you definitely want modulate how fast it comes back. By most estimates, naturally, it will take about 1000 years for the ocean and atmoshere to come back into equilibrium.
Another way to look at it is hurricanes were occuring before there was global warming. A big storm can move as much as 200TWh and there are as many as 21 of these on averages each year plus a lot of smaller storms. They are derived from the same source of energy as OTEC. They can keep producing in spite of moving such massive amounts of heat because most of that energy is returned back to the source in rain. It seems to me OTEC would recycle the heat it moves to the depths as well only over a much longer time scale.
Thank you for the thoughtful question however and thank you for being civil.