Most End-User's shouldn't be concerned with cold junction compensation since most modern day electronics that are used to monitor the EGT probe have this function built in so it is transparent to the End-User.
Thermocouples operate from a principal regarding dissimilar metals forming a junction that can be used to measure temperature. The primary (or "hot) measuring junction is the tip of the sensor, but secondary junctions are formed when the thermocouple is terminated to your electronics (usually copper wires here). This is typically referred to as the "cold" junction, since you do not want to measure the temperature at this termination point.
The temperature at this "cold" junction has to be measured to remove the offset to the measurement at the "hot" end at the tip of the sensor. If no "cold junction compensation" circuitry is used then your measurement would always be the ambient temperature at the termination to the electronics. The compensation circuit takes the ambient temperature measurement at this termination point out of the equation.
The Cold Junction is measured at the very end of the long wires (red & yellow leads). This point of measurement is typically done where the thermocouple (or, the Muffler Clamp Probe) connects to the measuring electronics.
