You can measure thermal conductivity by using ultra fast transient technique recently used by B. E. Belkerk et.al. for films in wide thickness range nm to micrometer. Consult their recent research paper published in Journal of Physics D: Applied Physics Vol 45 No 29 year 2012.
The problem is the temperature range, I think this is a great topic, since there is few works about the measurement at that high temperature (2500 degree), the metallic tranducer maybe a problem. Rather difficult in that temperature
Do you know Wiedmann Franz law? Measure the electrical conductivity by four probe technique and then find the thermal conductivity of your sample using the above mentioned law. Mind that this method is true only for metallic coatings and not for thin films in general.
The Mirage Effect Technique can be used to estimate the thermal conductivity (Kc).
The thermal conductivity is obtained by comparing the experimental photothermal signal variation versus the square root of the modulation frequency to the corresponding theoretical one.
210. Efim Litovskya,[1], Jacob I. Kleimana, Michael Shagalova, Robert B. Heimannb,1
Measurement of the thermal conductivity of cold gas dynamically-sprayed (CGDS) coatings between + 150°C to - 200°C. New test method and experimental results. Surface and Coatings Technology 242 · FEBRUARY 2014