  We investigate the critical speeding up of heat equilibration by the piston
effect (PE) in a nearly supercritical van der Waals (vdW) fluid confined in a
homogeneous porous medium. We perform an asymptotic analysis of the averaged
linearized mass, momentum and energy equations to describe the response of the
medium to a boundary heat flux. While nearing the critical point (CP), we find
two universal crossovers depending on porosity, intrinsic permeability and
viscosity. Closer to the CP than the first crossover, a pressure gradient
appears in the bulk due to viscous effects, the PE characteristic time scale
stops decreasing and tends to a constant. In infinitly long samples the
temperature penetration depth is larger than the diffusion one indicating that
the PE in porous media is not a finite size effect as it is in pure fluids.
Closer to the CP, a second cross over appears which is characterized by a
pressure gradient in the thermal boundary layer (BL). Beyond this second
crossover, the PE time remains constant, the expansion of the fluid in the BL
drops down and the PE ultimately fades away.
