I am talking about the ice which was lost (volume) according to the presented above graph, between June 1st 2015 and June 27th 2015, which my eye balls tell was nearly 8200 cubic kilometers. I.e. i am calculating energy which was already spent, to melt ~-1,8C sea ice into ~-1,8C sea water. The amount is significantly higher than "average" for last ~15 years. The difference between June 1...27 of 2013/2014 and June 1...27 of 2015 - amounts to nearly annual mankind's energy consumption, give or take. I.e., it is as if all energy 7+ billions of humans spend during a whole year - was sent there to Arctic to melt more ice in just one month, June. Unless the graph is wrong, this has already happened.
Personally, i suspect a) early massive drops of sea ice/snow albedo and b.) warmer than usual sea water under much of Arctic ice being two significant causes of this June's extra melt.
The a) was at least partially caused by massive early forest fires, such as Russian fires in April, which were massive enough to even spawn
event's own wikipedia page. Amount of soot and dust from such massive early spring fires is massive, and at least some of it, i believe, ends up in Arctic after a few weeks, decreasing Albedo, allowing the Sun to melt faster/more ice than usual. And as you can see on the satellite photo in said wikipedia arcticle, huge amount of smoke was going nearly northwards.
It still takes some time for it to be seen as "melt", though, - as decreased albedo first works much to produce faster temperature growth within the ice itself, and only after lots of "still cold from winter times" ice arrives to melting temperature, do we see extra fast melt per se. On the graph, we can see that May was rather average, which is exactly about the period of time when extra heat absorbed by Arctic is spent much to extra fast heating from much negative into near-zero temperatures - which contributes exactly to extra fast June's ice volume loss seen on the graph.
The b.) takes its roots in 2014, when we had several months bordering El-Nino. I was looking at Pacific currents back then, and it was my impression that it takes some 6...10 months for "warmer than usual" waters from sub-equatorial regions to travel "most of the circle" and thus arrive to regions next to Alaska, and thus affect weather patterns and water temperature there - which, of course, affects Arctic. Which i guess is happening right now.
As for future melt - yep, condition of the ice is important, weather is important, but it is my belief that whatever state ice is in, if you imagine 18g of ice (as a solid piece, or as many fractured pieces, any size), - then it would still take ~6010 Joules of energy to turn that amount of ice into same mass of liquid water. Fractured into pieces, ice would melt faster, yes, - because total surface of many pieces which together are 18g of ice mass is greater than surface of a single 18g piece of ice. But it doesn't change amount of energy which is needed for that amount of ice (18g) to melt into liquid water. It only changes how fast that energy could be applied to the ice, all other conditions being the same.
This is how i think these bits of physics work. Please do correct me if i am wrong somewhere. Hopefully, i am not.