Sorry but I disagree with your method.

You've taken an energy loss for the period 1995 to 2012(?) and applied it instananeously to temperature by calculating the effect of that net energy losses impact on temperature through specific heat capacity. ...

The way I've done it is to calculate the climate forcing implied by the energy loss .

...

Note that if you divide your calculated 0.4 degC by 18 years, you get 0.022degC, which considering the very different methods of calculation, isn't too far from my 0.006, only a multiple of 4.

...

I've no problem with that. My calculation is really rough and coarse and only showed, that the energy consumed by the ASI melting is really a factor to recon with. And a bad hypothesis, that triggers an insightful process is often how research and understanding works.

If we map the energy flow system by a network of capacities and resistances in steady state, and change somewhere something, there will be a transient state, after which there will be reached a new steady state. For the new steady state, only the resistances are of importance. This is Your approximation using the climate forcing and its effect on surface temps, which reflect the complex reaction by just one number: 0.75 K/(W/m²).

My approximation was more or less ignoring all resistances and steady state flows and taking only the capacities into account.Although the forcing approach is better then the pure heat-content-approach, it is not perfect. What You did is to add an artificial heat flow in the flow network.

The line thickness is roughly proportional to the thermal power flow they represent.

My point is, that it makes a difference for the temperature response, where You put in the extra heat drain.

Approximate the network further by two thermal resistors:

R1 from input point to the arctic (via atmosphere and ocean)

R2 from arctic to output point ( space) via vertical convection and radiation,

a thermal power input P.

Then the total temperature against space is given by P (R1 + R2).

So if I add some minor power p, the temperature difference is given by p (R1 + R2).

In our case, p is negative.

If I add p in the arctic, the temperature difference is only p R2.

This means, that for heat flows added somewhere inside the network, the sensitivity is lower.

Also, there is the question of the time constant. You wrote "hansens fast climate sensitivy". Would You be so kind to give me a link? What does "fast" mean?

So both envelope calculations are somewhat flawed. Interestingly, Hansen et al.: Earth's Energy Imbalance and Implications.. (seaice.de's link from above) delivers about the double value of Your forcing stemming from ASI melt. They took into accout not only the melting enthalpy, but also a temperature rise from -10 to +15 °C. But this doesn't make up for the difference.

In the picture drawed by the paper, the heat uptake by ASI melt is only roughly 1/4 of the total non-ocean heat uptake, with a distinct rise in the "hiatus" period, though. The other components are either wildly oscillating or show a slower, more continuous rise, while ocean heat uptake seems to have

decreased in the period in question! So IMO the importance of ASI melt for the rest-of-world-hiatus is supported.