To the question before us - yes, my cord gets fairly warm. It is a design choice -- the HPWC uses #6 wire rated at 105 degC insulation, which can carry up to 85 amps. Thicker wire would be harder to handle and store. Unless it's too hot to touch and becomes a safety issue for a contact burn, you shouldn't have to worry about the electrical safety.
Heat dissipation across a resistor is measured as power, but the V in P=IV is the voltage *drop* across a resistor, not the potential offered. So it doesn't matter whether it's 240V or 250V or 208V. As a result, the heat dissipated by a conductor varies with the square of the current (combine P=IV and V=IR and you get P=I^2*R). So the heat dissipation in the cable is 78% more with 80A over 60A.
If this were a DC circuit, the 25 ft of #6 used in the HPWC would dissipate 128 watts (2 conductors * (80A^2) * .01 ohms). AC introduces some complexity because of the reactive load of the battery chargers and such. Let's just say 100 watts of heat -- that's not insignificant.
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True but I was answering the question why voltage matters. You see it all the time - people don't understand that it's power into the car and power is the product of V and I.
As I mention above, the voltage supplied to the car does not matter here, because power dissipated is the voltage
drop across a resistor, not the voltage supplied. A given length of wire will dissipate the same amount of heat by a current-controlled circuit, whether it's supplied at 5v, 50v, 500v, or 5 kV.