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Try looking at what the internal geometry of cylindrical cell looks like first before making totally wrongheaded analogies. There isn't a wire going down it. It's a rolled thin film cathode/electrolyte/anode.
He is point is quite clear to me (he is not saying there is a wire, but it can be thought it that way in terms of conducting heat), but it seems to have flew over your head. JRP3 has discussed cells previously and it's extremely clear he knows all about the the jelly roll structure. It's actually a very good point that I missed previously.
What he is saying is that for the bottom cooled cell, the thermal interface has contact with all the anode and cathode layers directly.
In the old design, it only has contact with the outer layer and has to go through all the separator layers to reach through all the cell layers. From the own diagrams that you attached, you can see going from center to the outer layers of the cell has as much as a temperature gradient as going from middle to top even thought the distances are much shorter. This is likely because the separators serve as thermal insulators that slow down the spread of heat.
A picture tells things better so I have made a diagram that shows the differences:
The orange square part is the old thermal interface. You can see that it only will have contact with one layer and has to go through many separator layers to reach the middle.
The blue circle (the wider part representing the larger 2170 cell) is the new thermal interface. It has a direct path (no other layers in between) to every single layer in the cell.
If you rolled out the jelly roll into a flat sheet to see the thermal gradients, I'm not seeing how it's entirely clear that the old design would be better than the new, esp. once you factor in the separators.