The short answer is to change what the thermocouple amplifier is sensing.
You add a signal to each side of thermocouple amplifier input based on current power applied to cancel effect of power applied.
You will have inputs of = +power + -power + thermocouple.
The + power & - power will cancel leaving thermocouple value.
Need an example to make it clearer.
A battery has an internal resistance. You can not directly measure that resistance with a meter. If you measure the current power a battery is producing( the voltage & Current) and quickly change the current, the battery's internal voltage will be slow to respond.
The two voltage & current readings lets you compute the internal resistance.
Your thermocouple acts like a low voltage battery.
By changing power to heater quickly you can expose values.
Think of your setup
You have a heater resistor in series with thermocouple in some fashion. You have a voltage divider.
You can create a very low power matching copy of heater by scaling the resistors.
To measure power to heater block you need to add a current sense resistor.
Heater = current sense resistor, heater resistor, thermocouple.
Matching copy = 100x current sense resistor, 100x heater resistor, thermocouple.
Note that with the copy having 100 x the resistance, the heating change will be less.
When both chains are driven from same power source, you can compute the temp change of resistors if you change power level.
You have one thermocouple that changes based on heater block.
You have one thermocouple that reads room temp.
The copy thermocouple could be replaced with a resistor.
Note that if you connect your thermocouple amplifier to have one input being the heater block chain and other input the copy chain you can get the power cancel.
You have added two current sense resistors, one or two power sense inputs and a pot.
To check this out you might want to replace the second current sense resistor with a pot.
You want the voltage across both current sense resistors to match.
As power changes you adjust the original pot for 0 Change.
If power source to heater is AC this is easy.