This report describes the final tests carried out on an advanced apparatus for measurement of thermal conductivity of materials at atmospheric pressure and different levels of evacuation. The apparatus was designed and constructed in the phase 1 of the project. Difficulties with the control system have been solved and measurements have been carried out on common polystyrene foam insulation at atmospheric pressure. The measurements have been compared with results from reference measurements and a difference of only 0.3% was found in measured thermal conductivity. Measurements on monolithic silica aerogel were performed at 5 different pressure levels in the range 0.2 - 1000 hPa. The measured equivalent thermal conductivity is in the range 8.9 - 16.4 mW/(m K) which corresponds very well with results obtained by institutes in Germany and France.