We measure the radial and axial temperature gradients in a steady-state thermal conductivity experiment.  After calibration, the axial gradient is determined to be -0.221°C/cm, while the radial gradient measures -0.0045°C/cm. Under the assumption of linear temperature distribution, the temperature difference between the upper and lower surfaces of the test sample at thermal equilibrium is reconstructed. Additionally, the time-dependent heat dissipation rate of the cooling disk is quantified. The results demonstrate that the thermal conductivity of the sample is 0.157 W/(m·K), representing a 6.0% improvement in measurement accuracy compared to conventional methods.