Support for K couples would be great since they are the most common.
However implementing would be a pain in the ass.

Problem 1:
This is because thermocouples measure the temperature DIFFERENCE (Seebeck effect) and not the absolute temperature. To get the absolute temperature you have to measure the cold junction (right at the connector) as well and compensate in the mV scale.
Besides that, 1mV is not 1 degC unfortunately.

Problem 2:
I doubt if the Mooshimeter has enough stable digits to make temperature useful. Since a K couple has sensitivity of approximately 41 µV/°C

Problem 3:
The curves of thermocouples are not linear you have to compensate in the lower range and the higher range with coefficients.
These are a little bit different for every couple but not very important for low-end measurements.

See en.wikipedia.org/wiki/Thermocouple if you want to know more.
Also interesting: en.wikipedia.org/wiki/Triple_point
This is a very accurate reference at exactly 0.01 degC in which water consists in all 3 phases at the same time. (ice, water, vapor)