The scaling law in the scrape-off-layer (SOL) plasma is discussed, and the influence of the cross-field thermal conductivity, kappa , is analysed. Analyses are done for the edge temperature, temperature fall-off length and the fluctuation level. The dependencies on the heating power, edge density and safety factor are investigated. The scaling law of the thickness of the heat channel, which is crucial in evaluating the performance of the future large devices, depends on the model of kappa . It is found that the fluctuation level is most sensitive to the model of kappa . The importance of simultaneous observation on the temperature, gradient and fluctuation level is shown.