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 that it expands within the pores and causes dilation of the body. In that case, by analysing the kinetics of dilation during a change in temperature, it is possible to extract the permeability. The behaviour of an elastic porous solid was analysed previously. In this paper the case of a viscoelastic material is considered; for cementitious materials the effect of a 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.