Thermocouple differential output to thermocouple input
[I have posted a comment with practical questions.  In the meantime, here's a preliminary theoretical answer.]

Thermocouples measure temperature difference - inherently.  The temperature difference can be obtained without an additional OpAmp.



An important nuance is to turn off ice point compensation in the controller.

Further reading:
Differential-thermocouple temperature measurement system
Differential Temperature Measurement with Thermocouples