Heat transport plays a crucial role in igneous processes, and the thermal evolution of terrestrial bodies. Thermal conductivity (k) is a product of density (ρ), thermal diffusivity (D) and specific heat (CP). We measured D and CP as a function of temperature for a suite of planetary analog lavas relevant to the Moon, Mars, Mercury, Io and Vesta. Heat capacity was measured using differential scanning calorimetry on glasses and liquids covering temperatures from 400 to 1750 K; ρ was measured using the Archimedean method; and D was measured using laser-flash analysis on glasses from room temperature up to their melting point, which is slightly above the glass transition (Tg). Although the values of D and CP depend on both temperature and composition, we found no systematic variation of D with chemical or structural parameters. Glass data are described by the equation Dglass=2.305±0.22T−0.2567±0.015+7.796±6.2×10−5Twhere D is in mm2s−1 and T is in K, with 2σ uncertainty of 0.06 mm2 s−1. Thermal diffusivity of the tholeiitic liquids above Tg is Dliquid = 0.36 ± 0.07 mm2s-1, but the temperature-dependence cannot be constrained due to viscous flow and changing sample geometry at higher temperatures. The model for D presented here, in combination with already available models to calculate CP and ρ, allows prediction of thermal conductivity. For tholeiitic glasses, k decreases from ~1.5 ± 0.3 W m−1K−1 at ~295 K to ~1.3 ± 0.3 W m−1K−1 at Tg at ~1000 K. For tholeiitic liquids, k decreases from ~1.6 ± 0.3 W m−1K−1 at Tg to ~1.3 ± 0.4 W m−1K−1 at 1500 K. We recommend a generic value of 1.3 W m−1 K−1 for k of tholeiitic and basaltic lava instead of the commonly assumed 1.0 W m−1 K−1. Future work should aim to constrain the temperature dependence of D for liquids, for which a novel experimental approach is needed.