To observe the transport properties of a sample of warm dense matter, we used laser-induced fluorescence to measure the thermal conductivity of tungsten plasma confined within a rigid, ruby capillary tube. We determined the density and temperature of the plasma generated by an isochoric heating device using a pulsed-power discharge. The density was determined by the initial diameter of the tungsten wire used, and the temperature was obtained by spectroscopic measurements. The temperature of the ruby capillary was obtained from its fluorescence intensity, which depends on the temperature of the outer wall. We found the thermal conductivity to be approximately 30 W/K m, thus demonstrating that the thermal conductivity of warm dense matter states can be directly evaluated using the proposed method. Published by AIP Publishing.