Hi again,
Another interesting experiment...
If we connect three thermocouples in series then the center thermocouple wires will both be entirely at the unknown temperature T (ideally) if the measurement ends are not held at the known temperature. That means the center thermocouple will not have any temperature difference from one end of each wire to the other end of each wire so therefore will show zero voltage. So it effectively isnt even there 
Obviously that cant contribute to the voltage for the measurement.