Logic would dictate that your rationale was correct. The issue with welding fins on would also create hot spots where the mass off the pot were greater because of the fin. Think of it like the heat dissipation thing. Get a block of ice and place your finger in the middle. The whole block does not melt evenly because of the heat source (finger) but it does melt faster around that heat source.
I'd say no fins at all.
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