I had the wall charger with the 14-50 plug installed. Even with a 40A max set (which I believe was the limit for the device) it eventually started giving overheat warnings and dumbed down to 15A, the cord from the plug was hot to the touch. I even replaced the socket, using an expensive Hubell 9450 instead of the el cheapo Home Depot plug, same problem. Eventually Tesla replaced it under warranty, I now have a Gen 2 wall charger. (They don't make the one with the plug any more - presumably because of these sort of problems, I've seen posts suggesting this was not an unknown problem)
I installed the Gen2 with a 4' GE power cord and NEMA 14-50 plug, and this cord (and plug, and socket) stays cold to the touch under 40A load. But I made sure it was a 50-A rated power cord. (6Ga for the red and black, 8Ga for the ground, and for the neutral which is capped off not connected)
Also, make sure all connections are firmly screwed down...
the mobile connector, as I understand, is limited to 32A no matter what adapter.