I think it is worth remembering we are living on Earth not Mars... We have a layer of gas above ours heads which is not transparent to IR. Even in the old, dark, dry Arctic of the past it was impossible to radiate an infinite amount of heat to space. There is always an upper limit. A temperature inversion in the low layer, even in Siberia in the 1880s could not have been greater to ~ -25°C. At some point, even in an absolutely dark and dry Arctic a point of equilibrium will be reached. And on top of that amount of heat lost to space is not primarily a function of the temperature at surface, it is not the case, definitively. The temperature at surface is not totally decorrelated from the heat lost to space of course. But there is an atmosphere above surface, in the end. It is Earth here, not Mars... Heat has to go trough the atmosphere before, and there is on the road CO2, CH4, H2O in every states possible, etc... And now that Arctic is providing a lot of heat and moisture, we are seeing a new state where there is a layer of clouds and moisture in the low layers which is isolating the surface, with temperature between 0 and -5°C at 2 meters versus -20°C to -30°C at 2 meters in the case there is no clouds.
Holy mother of Einstein, it is Earth here, not Mars !
The picture which follows is the forecast for Saturday for a given model. It is the minimum for the temperature of brilliance in infrared (10.8 microns) for the all day. Scale is from blue for the warmest (~0°C) to white (~ -40°C) going trough the brown / beige / I don't know which color (-10°C to -20°C). There is also the isolign for the surface temperature of -2°C to roughly approximate the edge of sea ice (more or less, we all see what the shape of sea ice currently). Over Beaufort, yes we are radiating at 0°C (blue color) and we are losing heat to space. But over Chukchi, ESS, Laptev, Kara, Barents, we have a layer of clouds as thick as the troposphere. And the temperature of brilliance is -20°C to -40°C. The temperature of brilliance is more directly correlated to heat lost to space than surface temperature. This really means, this really means, that during the storm, we are not going to radiate heat toward space at ~0°C from the ocean. We are going to radiate heat at -20°C or -30°C or -40°C. And there is a factor 1.5 to 2 between the radiation from a black body at 0°C and a black body at -30°C or something. The heat stirred by the storm is heat at ~0°C, the heat lost to space is heat at -30°C, and there is a ratio of 1.5 to 2 between the two... I made the same map but with the mean of the IR temperature from Friday to Thurday. The ice sheet is high and dry, radiating at -30°C and isolating the ocean at 0°C below. The Beaufort is, yes, a good heat sink fully radiating toward space. But for the siberian side, the clouds are here as the ice sheet, isolating the surface below. Even with a mean over 5 days, almost all the siberian side is forecasted to be isolated.