See suitable methods

E. Litovsky, V. Issoupov, S. Horodetsky, J. Kleiman, Express Methods for Determination of Apparent and True Thermophysical Properties of Materials within a Temperature Range of – 150 °C ... 1800 °C, Proceedings of the 31st International Thermal Conductivity Conference and the 19th International Thermal Expansion Symposium, May 2013, DEStech Pupbl.

I. Fedina, E.Ya. Litovsky, M. Shapiro, A. Shavit “Thermal conductivity of packed beds of Refractory Particles: experimental results", J. American Ceram. Soc., 80 [8] 2100-2108 ) 1997.

You can take help on any thermal software and analyse the performance, as it is difficult to create such experimental set up for cyclic thermal loading,