Freegrass, I think you’re missing how the energy is transferred: it doesn’t happen by heating up the melt ponds and then having a thermal transfer into the ice or water, it happens by the melt ponds acting as lenses, so the solar energy instead of bouncing off the white snow, passes through the clear melt pond, through the relatively clear ice, and into the water underneath.
I don't think that this is how it works. The whole point about albedo of water being so much lower than ice (by a factor of 10 or so) is that water absorbs much more of the incoming radiation than does ice.
Because of albedo the ice under the melt pond recieves substantially less radiation than the surrounding ice. So I cannot see your explanation holding up at all. The water absorbs the energy and transfers it to the underlying ice at a steady rate, pegging the actual temperature at very close to the melting point of the underlying ice.
Same goes for a pot of water on a stove. If you put a handful of icecubes in the water, it will stay at 0C or near enough after you turn on the stove, and until the ice has melted. This is not because the water acts as a lense for the incoming heat from the stove, but because heat transfer in water at that scale is very efficient, and ice takes a hell of a lot of energy to melt.
Many of the melt ponds in that photo have melted right through the ice too, so they’re essentially open water now.
The image shows many melt ponds, a fair degre of leads with open water, and a few meltponds that obviously connect to open water. It's all in the colour of the water. And you can see the crumbled ice that Polarstern has left in it's past stretching up and to the left.
It should be possible to estimate the thickness of the ice surrounding the Polarstern based on this photo, I'd make a guess of an average thickness of 0.5 meters, not more. Which obviously does not fit with the thickness charts we have been seing from PIOMAS.
All in all it's a shocking photo - extreme melting obviously still ongoing, no compression of floes in spite of constant pack movement, and ice that is obviously a lot thinner than I would have expected.