Significant and persistent decreases in temperature have been observed in very porous materials when they are partially immersed in water at room temperature. As the sample sizes were much smaller than the maximum height of the typical capillary rise, this represents a far-from-equilibrium system. We attribute this thermal decrease to two concurrent actions: (i) the highly porous property of the material used; and (ii) a transition-phase-like process of the water. Thus, the water not only cools down the material surface through evaporation at the sample-air interface, but it also expands within the material, causing a further internal decrease in temperature that cannot be explained solely through evaporation. This latter process is persistent enough to maintain the decrease in temperature over time. This unexpected characteristic of water and its persistence when diffusing inside an extremely porous medium are the most original results of this study. Our results seem in agreement with the recent model on the fourth phase of water