I'm currently trying to measure the temperature of an off-the-shelf soldering iron. After realizing that the temperature-sensor in the soldering iron is a thermocouple, i ordered a type-K thermocouple ADC board, more specifically a MAX6675-based breakout board. While I am able to get temperature readings out of the chip, they are way to high in comparison to the real temperature. For example: I'm getting a reading of about 550°C, when in reality the iron has a temperature of slightly under 300°C.
Looking at this chart in the Wikipedia I think that my iron might be a type E thermocouple. https://de.wikipedia.org/wiki/Thermoelement#/media/File:Thermocouple_voltages.PNG
Now for the final question: Is it possible/feasible to convert/calculate the correct temperature (of a type E probe) from the type-K-thermocouple ADC reading? Has anyone done this in the past? I don't really need high absolute accuracy, +-10°C will be present due to the PID regulation anyway.
My last solution would be to order/sample a MAX31855E-chip from maxim and then swap the chip out on the board. I don't really want to do that, because the MAX31855E isn't that easy/cheap to source.
Additional information: I'm using an ATmega328 microcontroller, firmware is written in C, so any example code would be highly appreciated as well.