The effects of the STS 304 hollow cylinder property variations on the non-steady heat conduction are considered in this paper. In the non steady state, the specific heat and conductivity are depended on the temperature variations, and these properties affect to the governing equation on heat conduction. But the most of numerical analysis on heat conduction is assumed to constant properties which is conductivity and specific heat. Assuming that the properties are reacted sensitively, the numerical results can have the difference of between constant properties with non constant properties. The main parameters are specific heat and conductivity. The temperature distributions of the STS 304 hollow cylinder became in steady state after 4 minutes in case of the constant properties. As the conductivity is varied with temperature, the temperature distributions became in steady state after 15 minutes. Therefore, a numerical analysis of the non steady state heat transfer is so important in case of varying temperature.