Let's get back to the basics. The "battery cables" go directly from the battery to the motor, they are the thick heavy wires, typically two wires together.
The "wires" that go to the control box do two things, they provide a small amount of power to a few gauges (if there are any) and activate the starter solenoid, that's it. There is no high load associated with control box.
No wires should get hot when starting the motor unless it's wired incorrectly or the solenoid is bad.