Cottonwood
Roadster#433, Model S#S37
As a data point my HPWC cable gets warm at 80A but not hot at all. Maybe my voltage is 200V, not 240V.
BTW recently my Tesla only charges at 71A rather than full 80A, and I asked Tesla to check the logs. I thought my circuit's internal resistance or transformer capacity caused some voltage drop, but the engineer told me that my car's one phase of dual chargers is broken hence 71A. They offered me to change the on-board charger unit but I didn't ask because it's a minor issue.
However I thought "a phase is broken" seemed a little bit odd, since my circuit is 200V single phase, not three phase.
My guess is that you have 3-phase chargers where all three sub-chargers are connected in parallel. The 3-phase chargers seem to have about 10% more capacity than the single phase chargers. If I take 80 Amps * 5/6 * 1.1, it is 73 Amps; that is pretty close to your 71 Amps.
If I were you, I would have this problem fixed at the next regular service visit. One problem can sometimes be a warning of another to follow.