I've seen this at Corning and other places. In many cases, the handle was indeed quite hot. In at least two cases, it was barely warm and I still saw the reduced rate.
Yes I just came back from a 4500 miles road trip across the country. Over 30 Supercharging sessions. Sometimes the handle got hot, sometimes not, sometimes I saw a reduced rate, sometimes not. Most of the time, just unplugging and plugging back in increased the charge rate by 20-30 kW, sometimes it made no difference. At one Supercharger was a Tesla service guy who swapped out a cable. I charged at that stall (without anyone else there) and the charge rate was reduced. It's really inconclusive. I doubt it's a heat issue.
I also kept track of the battery temperature closely with TM-Spy. Interesting to see that at the end of the Supercharging session, the battery temperature was lower than before. In most cases the battery temperature dropped below ambient temperature at the end of the Supercharging session! The car is doing an amazing job cooling the batteries.
Once I arrived at a Supercharger with the battery at 51 Celsius (123 F)! Never seen it go that high from normal freeway driving. I got a reduced charge rate but the battery temp, again, dropped to 90 at the end of the Supercharge session.