The simplest way to measure thermal conductivity of a material is the divided bar. There are a number of commercially available systems that can do this measurement depending on the required accuracy and the nature of the material you are working with. Many of these units use the principal of the divided bar while a few of these units use a technique called hot disk TPS.

The simplest solution from what I have seen is the divided bar which You can as easily build you own if you are in a laboratory environment. 

http://www.tainstruments.com/products/thermal-conductivity-meter/

https://www.thermtest.com/laboratory-instruments-global

Dear Alexander,

Thank you for your answer. I have heat flow meter - Fox 600 and wonder if I can use this apparatus to measure impact of moisture on conductivity.

Best regards,

Piotr