Thermocouples work effectively by generating a delta voltage that represents the temperature differences between *two* junctions. The first is at the business end of the thermocouple. The other is at the end where the measuring apparatus is.
Most thermocouple amplifiers have a local thermometer, which they use to stake the temperature at the "local" end. So as long as the place where the thermocouple terminates (that is, plugs in) is at the same temperature as the temperature measuring thing for the thermocouple amplifier, you've got no worries.
If you improperly extend a thermocouple lead, then you've moved the termination point from where the amplifier is to the place where the incorrect extension ends. If that isn't at the same temperature as your reference, then your measurements will be wrong.
I learned all this from working on Toast-R-Reflow. I also make and sell a little AD8495 thermocouple amplifier breakout board that may help you if you're breadboarding a reflow oven controller.