This project covers the details of study, designing, fabrication and testing thermal conductivity testing apparatus for materials, such as Aluminum and Copper in low temperature range. This comprises a Hot Plate, which is the heat source, in the one side having Cold Plates at room temperature on the outer sides of specimen to cool down them. Heat from the Hot Plate is transfered by conduction mode from one side of the specimen to the Cold Plate on the other side. The temperatures as registered on the Hot Plate and on the cold Plate can be assumed to be the temperatures on the hot side and on the cold side of the specimen. By using this temperature difference, the thermal conductivity of the materials can be calculated. The work of this project can be separated into two parts. The first part is the study, designing and fabrication of the testing apparatus. The second part is the experiment to identify thermal conductivity.