Up top you have a closed system where the average temperature more accurately represents the thermodynamic temperature of the reservoirs, hot and cold. Below you have a Idunno system where the average temperature could depend on the boundary selection. If you leave a big enough gap so the average temperature represents the average energy of each reservoir, you reduce the size, i.e. heat content, of the reservoirs. If you get the total heat capacity right, you can blur or smear the average temperature so that it is less likely to represent the average energy. In other words, there would be some unknown amount of internal sinking.
Thermodynamics allow the luxury/burden of selecting reservoirs, frames of reference, that are most likely in something very close to thermodynamic equilibrium. Then all the laws of thermodynamics apply, provided your frames of reference are close enough to an equilibrium and/or steady state so that there isn't a lot of unknown energy transfer.
In my opinion, if you don't know for sure, pick another or several other frames of reference so you can compare and contrast results of the various frames. That is perfectly logical to me, but then who am I really?
If I can only get the results I want in one frame, then I might be wrong. To defend my choice, I would have to cleverly make up excuses for every thing that happens that should not happen. Remind you of anything?
Now if the krigers do publish some new results, let's see which crew has more excuses :)
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