Hello!
You cannot have a better resolution for free.
The thermocouple converter has a fixed range, apparently 0 ~ 1024 degrees. If you divide this
by 2^12 (or 4096), you end up to 1/4 degree, the 0.25 degree of the specs. And that's all.
You cannot have "a number for every 1mv". All what you will have is your reading +/- 2 degrees
in the 0~700 degrees range, and a bit worse above.
Now supposing that you have some random noise on your readings, you can use dithering in order
to get better resolution, at the expense of speed or delay. In this case, you can add 1 bit everytime
you multiply your samples by 4.
Dora