I keep my car in the garage of my house in Austin, Texas. The ambient temperature in there on a hot day can be 92F. (this is while it's in the mid-70's inside the air-conditioned parts of the house) My HPWC cable+handle already got replaced under warranty, last year. I had the exact same problems described above. The HPWC handle always gets very hot, and I typically keep a towel around that I can use to grip it and depress the button to get it out of the car. The end of the rubber cable that connects to the car plug was SO hot that I could not touch it without burning myself - that's when I measured it with one of those laser thermometer things and saw that it was like 135F.
The Tesla engineer agreed this was too hot, but he said something interesting - the cable itself has a design flaw (effectively) wherein it "bends" at the joint where the cable is going into the plug, due to the heavy bulk of the rest of the cable pulling downwards. That bend creates more resistance, which causes more heat (and undoubtedly causes the efficiency of the charger to drop below 92%, though that's hard to measure without metering installed)
Also, I was at a Texas vineyard recently that has a couple of "destination charging" HPWCs. (let me give them a plug, no pun untended,
Torre di Pietra | Romance of Tuscany, Wines of Texas!) The Texas summer sun was shining down and the ambient temperature was approx 103F. The entire cable was extremely hot while it was charging my car at 80A. The manager at the vineyard said they were still in the process of building out this area of the parking lot, and there would eventually be an awning over all this, thus getting it out of the hot sun.
The moral of this story is, "roll on liquid-cooled HPWCs" - I am sure Tesla is working on a new HPWC that sidesteps this whole issue. They may end up with a three tiered home charging product range - the "classic" or "some like it hot" HPWC, the new liquid-cooled "cool customer" HPWC, and the Tesla Snake.