Ultrahigh lattice thermal conductivity materials hold great importance since they play a critical role in the thermal management of electronic and optical devices. Models using machine learning can search for materials with outstanding higher-order properties like thermal conductivity. However, the lack of sufficient data to train a model is a serious hurdle. Herein we show that big data can complement small data for accurate predictions when lower-order feature properties available in big data are selected properly and applied to transfer learning. The connection between the crystal information and thermal conductivity is directly built with a neural network by transferring descriptors acquired through a pre-trained model for the feature property. Successful transfer learning shows the ability of extrapolative prediction and reveals descriptors for lattice anharmonicity. Transfer learning is employed to screen over 60000 compounds to identify novel crystals that can serve as alternatives to diamond. Even though most materials in the top list are superhard materials, we reveal that superhard property do not necessarily lead to high lattice thermal conductivity. Large hardness means high elastic constants and group velocity of phonons in the linear dispersion regime, but the lattice thermal conductivity is determined also by other important factor such as the phonon relaxation time. What’s more, the average or maximum dipole polarizability and the van der Waals radius are revealed to be the leading descriptors among those that can also be qualitatively related to anharmonicity.