I do not see a good reason to use an opap with an exremely high input impedance for the thermocouple.
Thermocouples generate small voltages, but their output impedance is generally quite low.
In some applications, even a stack of thermocouples (called a Thermopile) are used as an electricity source, and they can generate kilowats of power.
I do find the circuit odd.
Some things I do not understand is the generation of a separate power supply with Zener D1 and Series resistor R14.
You've also got an opamp left over.
If you buffer the zener voltage with the opamp, then you have a signal you could use as a "Zero" reference for the thermocouple. If you do that, you can use the ubiquitous TL072.
How much do you understand of how this circuit works?
Can you describe the function of each opamp?
I do like this circuit, as it's a very simple circuit and fit for beginners who are learning electonics by doing and want to build something useful.
I also find the circuit around the Triac and MOC3041 overly complicated.
Also, using 24Vac on a LED is not nice. LED's do not like reverse voltages.
That whole part can be exchanged with a decent MOSfet to switch the soldering Iron from the DC bus, but this does require that your bridge rectifier can handle the current of your soldering Iron.
Because of the simplicity and there is no cold junction compensation, your "room temperature" is your reference. Make sure to keep the cold junction away from any part that can get hot. (Even your hands).
A good calibration point is to adjust the circuit to the melting point of your solder. (Different types have different melting points, so look at their specification).