In college physics experiments, steadystate method, quasisteadystate method, and constant power heat source method are commonly used to measure the thermal conductivity of materials under normal and hightemperature conditions. However, the measurement of thermal conductivity of materials under lowtemperature conditions is not typically covered in college physics experiments. Based on the unsteady heat conduction theory for onedimensional semiinfinite objects under the firsttype boundary condition, using liquid nitrogen as a constanttemperature cold source, a device was designed to continuously measure the thermal conductivity of materials at low temperatures within a wide range，which provide a new approach for measuring the thermal conductivity of materials at low temperatures. Taking the measurement of the lowtemperature thermal conductivity of ice columns made of pure water as an example, the experimental principle, method, and device were elaborated in detail, and the measurement data were analyzed. The thermal conductivity of ice was measured within the temperature range of 10.49°C to 126.70°C. Due to the deviation of the correction model and the heat leakage of the device, the rate of change of thermal conductivity with temperature is higher than the reference value. It is hoped that further optimization of the experimental methods and devices will be carried out to improve the accuracy of experimental measurements.