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The thermal flash technique was utilized for measuring the thermal conductivity of vapor-grown carbon nanofibers and graphene nanoplatelets. The vapor-grown carbon nanofibers with stacked-cone morphology and heat treated to 1100 °C and 3000 °C were measured to have thermal conductivities of 1130 W/m K and 1715 W/m K, respectively. The physical dimensions of the constitutive cones determining the mean free path due to static phonon scattering were estimated to be ∼128 nm and ∼176 nm for the low and high heat treatment temperatures, respectively. Static scattering lengths shorter than the Umklapp scattering length indicate ballistic transport within individual cones and limit the thermal conductivities of the nanofibers. Additionally, nanoplatelets of few-layer oxygen intercalated graphene and multi-layer reduced graphene exhibited thermal conductivities of 776 W/m K and 2275 W/m K, respectively. The lower thermal conductivity of few-layer (∼3 layers) graphene is attributed to the presence of intercalating oxygen atoms which introduce covalent character to the interlayer interactions, acting as phonon scattering centers and hence reducing the phonon mean free path. The thermal conductivity measured for multi-layer graphene with ∼30–45 layers lies within range of the thermal conductivities previously reported for bulk graphite.