This research aimed to compare the transport capacity of loose-fill mineral wool, cellulose fibers, and wood wool to transfer moisture under steady-state conditions. The tests were carried out in the heat flow meter apparatus, which created a constant thermal field, limiting samples of sorptive moistened materials. The thermal conductivity, stabilization time, and moisture content of the samples were measured. Based on the variation in the results, the dynamism of moisture transport in the materials was determined. Mineral wool samples showed the lowest sorption. As a result, the moisture transport in this material stopped the fastest. In the case of cellulose and wood fibers, moisture transport continued throughout the whole test procedure. It was noted that the amount of moisture transport is influenced primarily by the structure of the fibers, the moisture content, and the possible presence of air in the pores. The wetter the material, the faster the transport. The dynamism of moisture transport according to trends of thermal conductivity changes over time was analyzed. The greater the slope of the linear regression line, the greater the dynamics of change. The smallest dynamics of change were found for mineral wool, for which the measured slope was between −0.008 and −0.033. For cellulose and wood wool, the range of slope was from −0.141 to −0.210, and from −0.162 to −0.211, respectively. The results of this research may provide the basis for further work on buffering moisture in the adjacent internal layers of the frame walls.