How to measure differential temperature of two locations by using two thermocouples
By using two thermocouples. Place it in parallel, + to + and - to -Measure the two hot junctions. The difference between the two hot junctions is measured. And if you want to measure total temp, just place the TC in series.T1 to Tn is the total output temperature.
Yes, measuring the differential temperature from two different thermocouples (of the same type) is possible, but not as described above.
The correct method is to connect the thermocouples in series, but with reverse polarity:
(AI is the analog input and presumably does the cold junction compensation):
AI (+) connects to T/C 1 (+) T/C 1 (-) connects to T/C 2 (-) T/C 2 (+) connect to AI (-)
Connecting thermocouples in parallel will produce an average temperature, not a differential temperature.
Connecting thermocouples in series produces a thermopile, which is of little commercial value for temperature measurement because there is no means to determine which temperture contribution comes from which thermocouple.