Ah yes and you solder that wire to the electrodes that will also need the insulation of the wire to withstand the higher temperature.
The electrodes receive a fraction of the heat that is generated at the weld spot, I don't see that we can do anything against this. When welding at higher energies like 100J, they, the electrode holder, and the connecting cable will indeed get quite hot. I alreday have this on my improvement list, because I think that some form of cooling and/or a better heat insulation for your hands is advisable.
available if needed to lower the resistance even further
Be careful when further lowering the resistance. In this application you are basically short circuiting a battery, and there is nothing except battery ESR and the cabling that limits the current. (The power switch is negligible with <0.2mOhm) The welder will go into overcurrent as soon as 2kA is exceeded. And I haven't done robustness testing at this current level yet, only at 1.5kA. The stored inductive energy will almost double from that (E = L * I^2 / 2).
jumpstart his wifes car ... some people that read this will burst in tears.
If I get this correctly if you have 4 supercaps in series and charge it with a controlled Voltage of 10V, still one of the caps might get more than 2.6V due to imbalances in the capacitors?
Exactly. There are two contributing factors to this. a) of course the capacity variation between them, b) variations in leakage current that causes them to self discharge.