So what evidence would you look for to prove that a massive heat influx is actually taking place?
Well, if you have winds coming from areas with temperatures much above freezing, than this heat must go somewhere, when it is tranported to the CAB. Wind speed, direction and the areas where it comes from can be seen in model outputs like at nullschool, where you clearly can see that higher temperatures are correlated a lot with wind speed, direction and source area.
You can also look at winds not only at the ground, but also in different heights in the atmosphere, e.g. at 1000 hPa and 850 hPa, where there is often a much bigger transport of warm air, which is at some point mixed into air at lower elevation. And if that warm air cools over the CAB, that heat must have gone somewhere.
https://earth.nullschool.net/#current/wind/isobaric/850hPa/overlay=temp/orthographic=-20.72,79.27,688/loc=-171.793,71.638And if you have clear skies with a lot of insolation, then obviously also a lot of heat is transfered through radiation and that heat must also go somewhere.
If that much heat wouldn't go into melting the ice, we would see temperatures probably over 20°C in summer heat waves on the pole. And this is not unrealisitic, when you look at Alert on Ellesmere Island, which sits at 82°N, and it reached 21°C this year, despite that a good amount of Ellesmere Island is covered with snow and glaciers and surrounded by sea ice. The few ice-free land up there was enough, to warm the air to such a high temperature. You can see that in model output e.g. at earth.nullschool.com
So that there is a lot of heat influx, is IMO very clear in a certain situation. What is much more difficult would be, to quantify that, to get a grip on how much Joule of energy went into melting ice and how much ice would that melt and how much will be absorbed by the ocean (which partly will also go into bottom-melting later). But this is very likely stuff, that models like PIOMAS will do. Because they must calculate, how much ice melted where, and how else would they do that, if not by calculating the amount of energy that possibly went into melting the ice.
