AVR Freaks

As Jim & John have said, use a thermocouple amp chip - as that includes the cold-junction compensation, etc.

Analog Devices is another manufacturer to look at; eg, as shown here:

https://www.electronicwings.com/avr-atmega/thermocouple-interfacing-with-atmega16-32  

https://www.analog.com/en/products/ad595.html

EDIT

That particular one is Not Recommended for New Designs (NRND) - but you get the idea.

Microchip are also in the game; eg,

https://www.microchip.com/wwwproducts/en/MCP9600

The likes of Sparkfun & Adafruit have a selection of breakout boards for these things - they tend to come with tutorials, examples, etc; eg,

https://learn.sparkfun.com/tutorials/max31855k-thermocouple-breakout-hookup-guide

https://learn.adafruit.com/therm...

The link above is a tutorial for a type k thermocouple interface you may find helpful.

Jim

For thermocouples, no doubt a thermocouple optimized chip is exactly what you need!  If you insist on using an opamp, instead of the decent TL072, there are now many single supply chopper-stabilized amps that are amazingly cheap and have microvolt (or better) offset.  Sadly, they have low bandwidth, but I doubt your temperature is gonna swing around at 8 KHz.  The progress of opamp specs with falling prices is pretty amazing. 

A friend of mine uses 50MHz opamps & never gives it a second glance (the equiv of ho-hum, let me pick up some beer & a 2Tb drive while I'm at the speedymart).  I say why are you usng such expensive parts & he says something like they are only 25 cents.

Indeed, Kartman's link is for a chip that does exactly what the  OP needs. There are really TWO issues here, neither of which is trivial:

1. The voltages are low. Few op-amps, even rail-rail ones, really work well with single supply and such low input common-mode voltages. And, those that do still have temperature drifts that can really corrupt the signal at low temperatures (say below 100C). Chopper-stabilized amps can do the stability job and, designed for the task, can handle the common-mode range of the input. But, it still takes care to do a reasonable design.

2. COLD JUNCTION. Let me repeat that! COLD JUNCTION. The voltage generated depends on the temperature difference between the warm end of the thermocouple and the cold end. The standard thermocouple tables are based on a cold end temperature of 0C. Anything warmer results in a measurement error. Again, if the measured temperature is below 100C or so, this can be quite significant. In fact, in a typical situation, the error will be on the order of 25C for any warm end temperature. 

A thermocouple interface IC, no matter who makes it, will solve both problems. It is a non-trivial exercise to solve both problems with general purpose op-amps and support circuitry. 

My recommendation: use a properly designed thermocouple interface IC. Does not make much difference who makes it. What does make a difference, a big difference, is that it is designed for that purpose with proper cold junction compensation.

Jim

You only need three things to implement accurate TC measurements:

1) A good chopper stabilized/zero drift op-amp, maybe spend as much as a dollar on it 8)

2) Cold junction temperature sensor, LM50 or LM60 for example, many options here

3) Charge pump to supply V- to the op-amp (two diodes and two capacitors)

Optional, a nice external voltage reference to eliminate the headache of using Avr internal references

MCU resources used: 2 analog inputs and one digital output

Mount the cold junction sensor "thermally close" to the TC terminal block

"Software" can give you linearization and compatibility with any/all thermocouple types