We started to develop a new certified reference material for specific heat capacity measurement using a new type of cryogenic adiabatic calorimeter, applying a pulse-tube cryocooler in the temperature range from 50 to 350 K. A candidate certified reference material is singlecrystalline silicon. To check the performance of the equipment, we measured the specific heat capacity of NIST SRM720, a type of synthetic sapphire. The relative expanded uncertainty of the measurement was estimated to be 0.65% at 350 K and 8.2% at 50 K, and the certified value of SRM720 was within the limits of uncertainty. In the next step, we measured the temperature dependence of the specific heat capacity of singlecrystalline silicon. The result was compared with some reference data, and good agreement within 0.6% residual was found.