How hot is "hot"? In general the inductive reactance heating is not a real issue until you have 300-400 amps of current.
Even though the manufacturer's tables will often show that conductor at 405 amps, that is in free air and at 90°C....very unlikely you are permitted to use the cable at that ampacity for any NEC application. There may be some applications where you could use it at 380 amps, but for most NEC applications, you will be limited to 230 amps, and that should not result in excessive heating where a single conductor is run through ferrous metal.
Note that both the enclosure and the cord grip, if made of ferrous materials will contribute to the inductive heating.