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. Previous papers have examined the behavior of an elastic or viscoelastic (VE) porous solid subjected to a thermal cycle slow enough to avoid internal temperature gradients. However, for cementitious samples, the sample size must be large enough that thermal gradients are likely. In this paper, we show that the effect of the gradient can be readily incorporated into the analysis of experimental data. For cement paste, experiments reveal that VE relaxation has a greater influence on the results than the gradient in temperature.