This is linear, but only if the thermocouple is linear.
Basic TMP35 sensor: α=41°CμV. (used for compensation)
Using this structure (thanks to both sensor and thermocouple) we go from the original sensitivity which is 41micro volt per degree, to a larger sensitivity which is 10millivolt per degree.
So this is an example and it is a complete instrumentation amplifier and thermocouple called junction compensator on a monolithic chip.
You only have to add the thermocouple, which is the only external part here, everything else is in the chip.
So it becomes a cold junction, so there is the need for a isothermal block, since you need to measure the temperature of this junction here, and this is performed by means of this internal voltage VR, “output” of the TMP35 (actually the output is a resistance).
At the end we have also this amplifier here which amplifies the voltage and we go from the original sensitivity which is 41micro volt per degree, to a larger sensitivity which is 10millivolt per degree.NOT_SURE_ABOUT_THIS (The increase in sensitivity should be mostly due to the termocouple)
This is linear, but only if the thermocouple is linear.