MAX31855 and Type K sensor seem to top down at -60°C (should be measuring -80°C)
The MAX31855 applies no linearization, the equation: 

VOUT = (41.276µV/°C) x (TR - TAMB)

is used. 

Thermocouples such as K are more-or-less linear so it's good enough for narrow ranges near where that average occurs. 

But if we look at the millivolts for type K with a reference junction of 0°C we get
an average of 40.03uV/K over -80 to +25°C so there is an error of about +3.2 degrees C resulting from the nonlinearity. 

You may have additional errors due to heat flowing down the thermocouple wires, as @Tony suggested in a comment, but there are other errors-

There is also a span error, which can be as big as 6°C over this range, and another 2 or 3 degrees C from the cold junction error. 



Make sure you have the thermocouple wired all the way to the terminal block with proper Type K thermocouple wire or thermocouple extension wire, connected with the proper polarity. If you use copper wire or have a double reversal, you'll have an error of 1-2x the difference in temperature between the two pairs of junctions. Use a small magnet to test the wires and join magnetic to magnetic and non-magnetic to non-magnetic, color codes vary from country to country. Usually, in North America, red is (-) and yellow is (+) for K.  The (-) is magnetic. 

Of course (+) and (-) refer to the voltage polarity when the tip of the thermocouple is hotter than the cold junction(s), in your case it will be the reverse.