Cold junction compensation can be one of a few methods, using either a diode or thermistor to read ambient at the controller and adding it to the measured voltage, or the more common thing done in these and simply assuming ambient is 25C and having a fixed offset. The fixed offset is quite common, as it does not worry too much if the ambient varies 10C either way, the variation in tip temperature in any case varies more just from orientation, or the amount of solder on the tip, along with it being in contact with the objects being soldered.
If you want true cold junction compensation you need either a simulated cold junction using a proper thermocouple amplifier and conditioner, or just add the scaled offset. Otherwise you need a cold junction with the melting ice bath and all to have the cold junction referenced to.