Arrays of ligand-stabilized colloidal nanocrystals with sizetunable electronic structure are promising alternatives to single-crystal semiconductors in electronic, optoelectronic and energy-related applications 1-5 . Hard/soft interfaces in these nanocrystal arrays (NCAs) create a complex and uncharted vibrational landscape for thermal energy transport that will influence their technological feasibility. Here, we present thermal conductivity measurements of NCAs (CdSe, PbS, PbSe, PbTe, Fe 3 O 4 and Au) and reveal that energy transport is mediated by the density and chemistry of the organic/inorganic interfaces, and the volume fractions of nanocrystal cores and surface ligands. NCA thermal conductivities are controllable within the range 0.1-0.3 W m −1 K −1 , and only weakly depend on the thermal conductivity of the inorganic core material. This range is 1,000 times lower than the thermal conductivity of silicon, presenting challenges for heat dissipation in NCA-based electronics and photonics. It is, however, 10 times smaller than that of Bi 2 Te 3 , which is advantageous for NCA-based thermoelectric materials.Colloidal nanocrystals self-assemble into NCAs with electronic and optical properties that can be broadly tuned by nanocrystal composition and size 1-4,6-8 . To be considered as viable replacements for traditional semiconductors, NCA-based technologies must also meet thermal management demands as high operating temperatures degrade device performance and lifetime. Thermal conductivity (k) quantifies a material's ability to dissipate heat and relates temperature gradient (∇T ) to heat flux (q) through Fourier's law, q = −k∇T . In metals, most heat is carried by electrons, whereas in semiconductor and insulating crystals, thermal conductivity arises from the transport and scattering of quantized vibrations that are born from the periodic atomic lattice, that is, phonons. Our NCAs are non-metallic and have a vibrational structure that is complicated by compositional heterogeneity and periodicity at two length scales: the atomic lattice within each core and the array of periodic cores separated by ligand monolayers. Studies of planar self-assembled monolayer (SAM) junctions show that surface chemistry can control energy transport at the interface between two solids 9 , but does it also influence the thermal conductivity of a bulk three-dimensional solid with a complex network of internal interfaces? We herein report on the hitherto unknown thermal transport properties of NCAs, using systematic thermal conductivity measurements complemented by heat capacity measurements and atomistic simulations.A series of NCAs was prepared with varying core diameters, core materials and ligand groups (Table 1) through spin-coating concentrated colloidal solutions onto silicon wafers 6 . During film