MAX 31855 and Thermocouple Errors

OK, (anyone who's still got the patience to listen!) here's the latest in my attempts to understand this weird thermocouple behaviour....

I've tried every combination of the following:

Libraries:
Cory J Fowler's library
George Matthew's library
Adafruit library
Rob Tilliart's library
(Many thanks to the above for all their efforts and help - it's much appreciated)

with...
A T-Type thin wire thermocouple
A K-Type thin wire thermocouple

and...
A 'BBTech' T Type amplifier breakout
A 'Playing with Fusion' K Type 4 Channel breakout
An 'Adafruit' 31855K breakout.

Everything seems OK at or around room temperature down to 0C, but my domain is in liquid nitrogen around -188C and warmer.

All the combinations (and an Adafruit RTD PT100) seem to give similar results, the attached graph (THERMO TEST.JPG) shows a calibrated meter (fitted with two K Types) against a 'BBTech' breakout fitted with a T type and a 'Playing with fusion' with a K Type (four actually and averaged). All the libraries give similar results.

The test involved dunking all the thermocouples into liquid nitrogen (-188C) and allowing to warm back up to room temperature whilst logging the output. This was repeated many times with different combinations of library and hardware.

After looking at the first graph, I worked out can 'fudge' the results by applying the following 'correction factor'

Corrected Reading = Actual Reading+(0.71*Actual Reading)

This results in the second graph (FUDGED.JPG) output, which is probably near enough for what I need, but I'm really like to know what the problem is.....

Any thoughts anyone?

Thanks....