In an attempt to reduce thermal resistance of heat storage material, carbon fibers were mixed with it. Paraffin whose thermal conductivity k(m) = 0.2 - 0.3 W/(m . K) and carbon fibers (k(f) = 25 and 220 W/(m . K)) were used. Transient temperature responses within the composite material contained in cylindrical capsules were measured in the melting and freezing stages. The volume fraction of the carbon fibers (X-f) was varied up to 1.1%. The fibers increased the melting period because they inhibit natural convection within the liquified paraffin phase. However, the fibers had sufficient effort on the reduction of the freezing period even at X-f < 1%. For instance, the freezing period of the composite where X-f = 0.5% and K-f = 220 W/(m . K) was approximately half of that with free of fibers. The effective thermal conductivity of the composite was moreover discussed based on the effective thermal diffusivity measured from the temperature responses.