Can two thermocouples of the same type measure the average temperature in series? Why?

Two thermocouples of the same type connected in series can't measure the average temperature.

Because thermocouple temperature measurement produces thermoelectric potential, two thermocouples of the same type are connected in series, which is equivalent to two thermoelectric potentials connected in series. This is superposition, which is theoretically twice the temperature (without considering the loss).