I believe the wire in question (red wire with tracer) is the resistor wire for the ignition. That might explain why it gets hot. When the starter is engaged, the solenoid puts a full 12v to the ignition (via green? wire). If you do an ignition upgrade (big cap), you can delete the resistor wire from the system and just use +12v from the IM (yellow wire). The coil would need to be changed to 3 ohm.
Thanks to everyone for their suggestions. Rollguy, I'm not sure I'm following you. I did the big cap upgrade years ago, and the yellow wire that is on the same post as the red w/ tracer is the one that got cut as part of that upgrade. The red w/tr is labeled as the resistor wire and hooks onto a yellow wire that goes to the actual ignition switch. What is the purpose of the resistor wire? Are you saying that because I did the big cap upgrade I may not even need it? Thanks again.
If you replaced the coil with a 3ohm coil (like the petronix one), then the resistor wire isn't needed and gets bypassed. If you are using a lower resistance, 1.4ohm, coil, then the resistor wire is still needed so that the ICM doesn't get burned out.