Simultaneous heat and mass transfer through a medium-density fiberglass insulation slab is studied using a one-dimensional transient numerical model formulated using the local volume averaging technique. The insulation is open to ambient air at a specific humidity on the warm side. The cold side boundary is an impermeable cold plate at specified temperatures. This study examines the effect of changing the cold temperature boundary condition on the predicted heat and mass transfer. The thermal performance of fiberglass insulation is poorer as the air humidity increases. This is particularly evident after a step change in the cold temperature boundary condition where, for an air relative humidity of 97%, the heat flux is 4.9 times greater than the dry case even though the accumulation of water is only 0.14% by volume (1.9% by mass) and the average effective thermal conductivity of the insulation has increased by only 3.5%. The effects of neglecting thermal hysteresis (characterized by both the difference between the adsorption and desorption isotherms and the heat of adsorption and desorption) in modeling transient heat and mass transfer in fiberglass insulation subject to a step change in the cold temperature boundary condition is studied. Neglecting thermal hysteresis is found to be significant at temperatures above and below freezing. The predicted mass transfer under hysteresis properties can be up to three times different than that predicted using non-hysteresis properties and the heat transfer can be influenced by as much as 20 to 30% for the few numerical studies presented in this paper.