Drying of porous media very often occurs in the presence of significant temperature gradients because heat fluxes are imposed in many situations in order to decrease the drying time or to facilitate the moisture removal at a higher humidity of the surrounding gas phase. Here we consider the situation where the temperature increases with depth. We show from experiments with a micromodel that the temperature gradient induces the stabilization of the evaporation front within the model porous medium according to two different mechanisms occurring consecutively. The first mechanism occurs in the liquid phase and is explained by the dependence of surface tension upon temperature. This results in the preferential invasion of the warmer zones. The second mechanism occurs gas-sided due to the dependence of saturation vapor pressure upon temperature. We show that the time scales of both mechanisms are different leading to the temporary formation of distinctive phase patterns from which different periods of drying can be discriminated.