When a porous material that is saturated with liquid is heated, the liquid typically expands much more than the solid phase; if the permeability is high, then the liquid flows out of the pores as it expands, However, if the permeability is low, then the liquid may not be able to escape, so it expands within the pores and contributes to the dilatation of the body; as the liquid drains from the pores, the body contracts to the dimension dictated by the thermal expansion coefficient of the solid phase. In the low-permeability case, by analyzing the kinetics of dilatation during a change in temperature, it is possible to extract the permeability. This technique, which previously has been successfully applied to gels, is also applicable to conventional ceramics, such as porous glass, sintered ceramics, cement, and concrete, However, for these rigid materials, the analysis must be modified to take account of the finite compressibility of the liquid. In this article, the thermal expansion kinetics are analyzed for cylindrical and platelike samples. The results are applied to cement paste in a companion paper.