A test anyone can run:
Look at the charging page on your app or the Tesla display. Plug in the power connector. Note the voltage right when you see the amps start out at low 1 or 2. Now wait till the amps reach 48 and note the voltage again. If it drops more than 10 volts you have a major problem. Watts equals volts times amps, so that would be almost 500 watts being dissipated in the conductors, and I am fairly sure less than 100 of those watts are burning off in the 18' cable!
I have about 25 feet of #6 from the 60A breaker to the TWC. I'm losing 6 volts across the current path. Wow. Charging starts at 241 volts, and as the current ramps up to 48 amps, it drops to 235 volts. Holy ****. That's almost 300 watts (6 * 48) being dissipated in the conductors and the cable. At 48 amps, the conduit gets warm after a couple of hours in a 65 deg garage. Wait till Phoenix summer when the garage is at 110! Scary. For reference the 18' TWC charging cable also gets warm-ish. I assume that's by design.
This is the answer I needed. Thanks! Much of the other info here is all over the place and seems to be theoretical and focus on saving a nickel or two at elevated risk. I'll go with the safe / code way. Again THANK YOU!! My electrician will be back out in a week to replace the #6 in 3/4" conduit with #4 in 1" conduit.
Those of you running Tesla Wall Connectors and charging at 48 amps, after 2 hours of 48 amp charging, please go out and feel the conductors that run from your 60 Amp breaker out to the TWC, especially if they are unprotected romex. If you feel more than gentle warmth, think about spending money (OMG!) and protecting your house and family.
The voltage drop is not just in the branch circuit, it is in everything up to and including the power company transformer. A 6V drop at 240V is only 2.5%. NEC guidance for feeder and branch circuit combined is 5%, with 3% for branch effects. #6 copper wire is 0.3951 mOhm per foot. Your 50 ft round trip branch circuit has a drop of 0.95V, 45.5W total. Less than 2W per foot. 5 volts of drop (83%) is due to the feeder to your breaker panel, the breaker, and charge cord.
#4 gas a resistance of 0.2485 and will give a drop of 0.6V and power loss of 28.6W.
#6 NM-B is undersized for 60A, but #6 copper THHN is not. As to warm to the touch, 60C is 140F, 20F hotter than the maximum water heater temperature. 75C(THHN) is 167C rated.