Fast and reliable methods for the determination of thermal properties of core materials for vacuum insulation panels (VIPs) are needed. It is of great importance to know the thermal performance of a VIP core at different levels of vacuum and external loads. In this study a new self-designed device, consisting of two cylindrical cavities connected to a Transient Plane Source instrument, is used to determine the thermal conductivity of low-density nanoporous silica powders, from atmospheric pressure down to 0.1mbar while applying different levels of external pressure up to 4bars. The study includes a brief theoretical discussion of methods. The TPS is validated through comparison with available data for commercial silica as well as through independent stationary measurements with a hot plate apparatus and with a Transient Hot Bridge method. The different materials illustrate clear but different trends for the thermal conductivity as a function of the level of vacuum and external pressure. The analysis of experimental results shows that the transient methods are less suitable for measuring the thermal conductivity of low-density silica powders, especially for the cases when the density is less than a limit at which the heat transfer by radiation becomes dominant compared to pure conduction.