I was once given the some circuit diagram of what you mentioned of in this discussion forum. I didn't focus on it because it won't be easy getting it in my country and for that reason I have to purchase it online and which will take almost 1 month to be delivered to you. That's why I want to work it out myself.I used a ready-made chip the AD595 for Ktype thermocouple gives out 10mV per degC.
https://www.analog.com/en/products/ad594.html#product-overview