Thermocouples give VERY small voltages at modest temperatures. You get a voltage differential of about 41 uV per degree C with type K. So, for a reference junction at 20 C, and sensing something at 220 C, you get about 8.2 mV. So, tiny voltage offsets will totally swamp the measurement.
You can get simple temperature controllers on eBay, and just ignore the control function and use it as a readout. (Or, you can use it as intended, with a solid state relay, to control the heater.)
You have to be crazy, in my book, to design a thermocouple readout circuit, it is just a HARD problem due to the tiny voltages involved.
Jon