There are ADCs like the LTC2418 that handle thermocouples fine.
A normal op-amp won't work well no matter how good a programmer you are!
The problem is offset, thermocouple inputs are so small that common opamp offsets might make hundred of degrees F of error.
Second thing here- is this thermocouple grounded? It's ok to do that, not only we can bolt both wires to a grounded cylinder head, in fact a thermocouple can even measure a temp on a grounded hot plate by bonding one wire at one point and the other wire at a different point! But this means one voltage is slightly above ground, the other slightly below, so we need to be able to measure slightly below ground AND we need to be differential.