Tthe Fontainebleau Sand often contains calcite crystallarias, the dating of which shows formation during the past two cold periods of the Quaternary, around 300 kyr and 50-30 kyr. They would be equivalent to the cryocalcites related to frozen karst cavities, but would have developed in the sand aquifer. They are sometimes included in the quartzite, suggesting that sand silicification also has to be related to Quaternary cold periods. In this context, we run a set of transient simulations on a typical 2-D hydrogeologic section of the Beauce Plateau using a fully coupled groundwater flow and heat transfer model with integrated freezing and thawing processes. The code takes into account latent heat effects and modifications of hydraulic and thermal properties due to ice formation. Our model calculations allow us to investigate the temperature and pressure conditions associated with permafrost propogation that could have prevailed in the valleys at the groundwater outlet.