Amplifying signal from the copper wires of two type T thermocouples
As long as you need the difference, you don't need a special thermocouple amplifier with zero point compensation.

The sensitivity of the T type thermocouple (copper-constantan) is 43uV/K, so for 20K difference you will have 860uV or 0.86mV range. If you have an ADC with 5V range it means you need a gain of 5814. 

This value is pretty high and you will need a very precise OpAmp in order to get acceptable temperature drift. 

But here comes the question of what accuracy you need? If you assume 0.1K accuracy and for example 20K difference in the device working temperature, you will need an OpAmp drift of 4uV/20K = 200nV/K or less, which means Auto-zero opamp.

Something like AD8676 (200nV/K) or AD8538 (30nV/K). 

Don't forget about the input offset compensation, AC noise filtering and the quality of the passive elements (resistors) that can ruin the accuracy of such small signal amplifiers.