In this work a new convenient experimental setup is made with the help of a Gifford-McMahan cryorefrigerator to study the variation of thermal conductivity with the temperature of any solid material in the range of 35-300 K. The GM refrigerator can produce a temperature down to 35 K with a refrigeration capacity of 29.20 W. The principle of this experiment is based on a guarded hotplate method. The thermal gradient along the thickness of the sample is achieved with the help of electrical heating in the range of 100-230 K. The sample has been insulated from the ambient heat inleak with the help of a vacuum of 10 -6 Torr and with a number of super insulation layers. Three samples of elastomer with different composition suitable for cryogenic appliance have been prepared in cylindrical shapes of 6.00 cm diameter and 1.2 cm thickness. The variation of thermal conductivity is studied at a mean temperature of 1 00, 120, 130, 1 50, 170, 190 and 210 K. From the experimental study it is seen that the thermal conductivity of all the samples increases with the increase of temperature and reaches a peak value in the range of 0.00165 to 0.00173 W cm -1 K -1 and then decreases, as temperature is further increased to a constant value. This is in full agreement with the published literature. The variation of peak values of thermal conductivity for different samples is found to be 1 to 6% with respect to the published data. This has ensured the reliability and accuracy of the experimental setup.