The simultaneous propagation of thermal and evaporation waves through a one-dimensional, water-wet porous media subjected to through-flow air drying is investigated through a set of theoretical, numerical, and experimental studies. The injection of dry air at a constant temperature, equal to the uniform initial temperature of the medium, is considered. Theory is developed for the limiting cases of i) a fast evaporation wave velocity relative to the characteristic thermal wave velocity, and ii) a fast thermal wave velocity relative to evaporation wave velocity. Mass and energy conservation equations are transformed to coordinates moving with the waves and the general energy transfer and drying behavior is described. Numerical simulations and experiments were performed for the two limiting cases plus one in which the evaporation wave velocity was approximately equal to the speed of the thermal wave. The numerical simulations and experimental data verified the basic features of the theoretical description. Theoretical, numerical and experimental results show that dryout times and temperature distributions in the one-dimensional porous medium were strongly dependent on the relative speeds of the thermal and evaporation waves. Contrary to conventional thought, the temperatures found in the porous matrix are not directly related to wet-bulb values. Under the condition where the evaporation wave velocity is equal to the speed of the thermal wave, a theoretical singularity suggests a very large temperature drop at the front; simulations and data for velocities approximately equal show the temperature at the front continuing to decrease with time to an extrapolated limit of freezing water.