The purpose of this work was to study both theoretically and experimentally the process of moisture redistribution and heat transfer due to phase changes during the tests of thermal conductivity in aerated autoclaved concrete (AAC) moist specimens. The different moisture contents of the test samples were obtained in climatic chamber at equilibrium conditions reached with constant air temperature and variable relative humidity. The moist specimens were sealed inside highly impermeable polyethylene bag, as required by UNI 10051, and placed in a heat flow meter apparatus. During the experimental thermal conductivity measurements, the temperature and heat flow rate were measured under transient and steady state conditions. A theoretical analysis of the heat and mass transfer process was performed and then a suitable numerical model was used to predict the moisture redistribution and heat transfer due to the phase changes. The theoretical model has been compared against the experimental data. Substantial agreement between numerical results and experimental data was found. Then several numerical simulations have been performed to study the influence of the errors due to phase changes and non-uniform moisture distribution during the test of thermal conductivity of moist AAC specimens.