Thermocouple reading different from Commercial Datalogger when using Arduino
A ten degree change would induce 50 millivolts of change on the output of the thermocouple board (or 25 mvolts after your divider).  This is a relatively small number.  I suspect a number of things that can cause errors of this size

First bet would be resistor mismatch.  If your 210kohm resistors don't match perfectly, what would your output voltage be.  Start by assuming one resistor is perfect, and the other is worst case off.  If those are 5% tolerance resistors, assume one is at 210Kohms, and the other is at 220kohms (for a roughly 5% error), and figure out what your divider really outputs.  Thumbnail calcs show that if you're measuring across the 220Kohm, a 5 volt input would give you 2.558 volts out, and there's your 50 mvolts!

Next, you may be having input impedance problems on your A/D input.  You have a relatively high impedance source (>100kOhms) going into a cheap A/D with modest input impedance.  Your A/D could very well be loading your voltage divider.

Precision measurement in this case calls for precision techniques.  If you build an op amp circuit (these have low output impedance) with an amplifier that has a very low input offset voltage, give it a gain of 0.5 (yes-- you'll have to invert to get a gain less than 1.0), and use pots to trim all the resistances and maybe offsets, you'll do better.

If you still want to do things this way, try using 1% tolerance (or better) resistors of much lower value, maybe 5kOhms.

As a last possibility, maybe there's an offset somewhere on your thermocouple board that you have little control over.  Thermocouples can be tricky to use correctly, and maybe their cold junction compensation isn't what it should be.

Also, you'll learn more about your error if you actually chart it across a temp range rather than a single point.  I recommend a slow transition between an ice/water mix at 0 degrees, to hot tap water at around 40.