When the transient hot-wire method is used to measure the thermal conductivity of very low thermal conductivity silica aerogel (in the range of 10 mW/m·K at 1 atm) end effects due to the finite wire size and radiation corrections must be considered. An approximate method is presented to account for end effects with realistic boundary conditions. The method was applied to small experimental samples of the aerogel using different wire lengths. Initial conductivity results varied with wire length. This variation was eliminated by the use of the end effect correction. The test method was validated with the NIST (National Institute of Standards and Technology) Standard Reference Material 1459, fumed silica board to within 1 mW/m·K. The aerogel is semitransparent. Due to the small wire radius and short transient, radiation heat transfer may not be fully accounted for. In a full size aerogel panel radiation will augment the phonon conduction by a larger amount.