Transient conduction on a vertical, constant heat flux surface in a saturated porous medium is studied experimentally and analytically with a focus on determining near-wall thermal diffusivity. For combinations of different particulate solid and interstitial fluid, which give a range of conductivity ratios, ks/kf, from 0.5 to 2400, the present study finds that early-time transient temperature profiles can be analytically predicted using the thermal conductivity of the interstitial fluid because the near-wall porosity approaches 1.0. The conjugate heat transfer analysis accurately predicts the time the conductive front takes to travel through the impermeable wall. The present study also finds that conductive heat transfer along the wall is dependent on the wall thickness and must be taken into account when assessing measurement of local and overall Nusselt numbers. The present results raise the possibility of reinterpretation of much of the porous medium heat transfer experiments that make up the current database.