Not much lives 1000m under the surface. Also, the amount of heat that we would send is actually quite small compared to the heat capacity of the oceans. Water has 4000x higher heat capacity than air by volume.

Transferring heat from a hot place to a cold place is really easy. In principle you can just connect them with a highly conductive material like copper. In practice even copper might not have enough heat conductance, so it might be better to pump either water or air from one place to another.