We have studied the dependence versus nominal composition and temperature of the thermal conductivity in the AlCoFeCr system close to the region where an approximant of the decagonal phase forms. This compound of the Al5Co2 type shows a melting temperature above 1100°C and is of interest because it dispays low thermal conductivity whereas its expansion coefficient is comparable to those of metallic substrates. Used as a coating, it is of potential value for the sake of producing thermal barriers. From a study of the occupied band by X-ray emission spectroscopy, we show that its poor thermal conductivity above room temperature fits with the recurrent localization scheme of electronic states.