When a porous material that is saturated with liquid is heated, the liquid expands much more than the solid phase. If the permeability is low, then the liquid may not be able to escape as it expands, so it expands within the pores and causes dilatation of the body. In that case, by analyzing the kinetics of dilatation during a change in temperature, it is possible to extract the permeability. T he behavior of an elastic porous solid was analyzed previously. In this paper, we consider the case of a viscoelastic material; for cementitious materials, the effect of relaxation is shown to be significant, but the elastic analysis will usually provide sufficient accuracy. If significant viscoelastic relaxation occurs, it is revealed by comparing the data from samples of different sizes.