We have performed a series of numerical simulations of heat transfer between lunar lava flows and the underlying regolith with the goal of determining the depths in the substrate beneath which implanted extralunar volatiles would survive outgassing by the downward-propagating heat pulse. Exogenous materials of interest include solar wind and solar flare particles, and the cosmogenic products of galactic cosmic ray (GCR) particles emplaced in the lunar regolith early in Solar System history. Extraction and analysis during future lunar missions would yield information about the evolution of the Sun and inner Solar System environment. Particles implanted in regolith deposits may be protected from gardening and saturation if buried by a lava flow, but must be sufficiently deep in the regolith to survive the consequent heating. Our simulations include detailed treatments of lava and regolith thermophysical properties (thermal conductivity, specific heat capacity), which vary widely over the temperature range relevant to lava flows in the lunar environment (~200 to >1500 K). Simulations adopting temperature-dependent properties, together with a treatment of latent heat of lava crystallization, indicate that implanted volatiles would be fully preserved at depths greater than 20 cm beneath 1 m thick lava flows, ~60% deeper than predicted by simulations employing constant properties. These results highlight the necessity of appropriate prescription of material properties. Consideration of the range of lunar lava flow thicknesses allows us to determine the range of depths from which pristine samples may be recovered.