The aim of this paper is the presentation of the method for thermal conductivity measurement and numerical modeling of temperature distribution in apparatus for measuring the thermal conductivity. Experimental studies will be carried out in transient state until the steady state heat conduction in apparatus is achieved. The calculated and measured temperature distribution will be compared. The time to steady state in apparatus for different samples will be estimated based on numerical and experimental results. The influence of the contact resistance between the sample and the measuring device will be analyzed.