The water in the deep oceans should not be measured as heat or warm. It has a minimum stable temperature point based on density and pressure. So you have to measure the volume of the minimum or the cold point volume. There are two primary metrics that affect cold point volume. Solar energy from above and volcanic heat from below.
The proper way to state what the AGW zealots are claiming - The cold point volume of the deep oceans is shrinking.
My 2cents anyway.