In this study, classical molecular dynamics with the well-known van Beest, Kramer and van Santen potential are used for the first time to investigate the solid thermal conductivity of silica aerogel. Aerogel samples at various densities are obtained through negative pressure rupturing of dense silica samples, and reverse non-equilibrium molecular dynamics is employed to determine the thermal conductivity at each density. Results indicate that a power-law fit of the thermal conductivity obtained varies almost linearly with density, where decreasing density and increasing porosity led to an almost linear decrease in thermal conductivity. This is reflective of the trend observed in experimental bulk sintered silica aerogel. The results also showed that the thermal conductivity is of the same order of magnitude as bulk sintered aerogel. The power-law fit of the results also accurately reflected the variation found in bulk sintered aerogel.