[thedoc (OP)]

Jim Meyer asked the Naked Scientists:
   
Hi, I guess you all know the Earth is very hot a few miles down below the surface. My question is how much heat flows into the ocean from the mantle through sea vents and volcanoes on the seabed? How much heat flows into the atmosphere through all the geothermal systems of Earth?   
What do you think?

[evan_au]

The graph here shows that the Earth releases around 0.4W/m² at the mid-ocean ridges, and much lower .(<0.1 W/m²) at regions which are not geologically active.
See: https://en.wikipedia.org/wiki/Earth's_internal_heat_budget

This is tiny compared to the approx 200W/m² of solar power which lands on the sea (averaged over a year).