Heat transport plays a crucial role in igneous processes, and the thermal evolution of the interiors of terrestrial bodies. Thermal conductivity is a product of density (ρ), thermal diffusivity (D) and heat capacity (CP). We measured Dand CPas a function of temperature for a suite of planetary analog lavas relevant to the Moon, Mars, Mercury, Io and Vesta. Heat capacity measurements were conducted by differential scanning calorimetry (DSC) on glasses and liquids covering temperatures from 400 to 1750 K, Dmeasurements were conducted by laser-flash analyses (LFA) on glasses from room temperature up to their melting point slightly above the glass transition (Tg), and densities were already known. Our results demonstrate that the variability of Dand CPis very composition-specific, making thermal conductivity (k= DρCP) strongly composition-dependent. We present an empirical model to estimate Dof glasses as a function of temperature and composition, with 2σ uncertainty of 0.040 mm2s-1. Thermal diffusivity of the corresponding melt can be calculated with an uncertainty of 0.044 mm2s-1, but only independent of temperature. The model for Dpresented here, in combination with already available models to calculateCPand ρ, allows to predict thermal conductivity for a wide range of compositions for glasses and melts relevant to major planetary objects in the solar system. We show that basaltic liquids have thermal conductivities between 1.0 and 1.7 Wm-1K-1, about half that of the mantle from which they are generated, and therefore partial melting of ascending mantle leads to a positive feedback that promotes high melt fractions. The chemical dependence of ksuggests that this effect may have been more or less effective on different planetary bodies and at different times in their evolution.