A grain silo is submitted to periodic and meteorologic influences : solar radiation, air temperature, wind. The heat transfer from the wall provokes a natural convective air flow and the grain out of equilibrium releases water. We consider heat and mass transfer in a cylindrical silo submitted to a uniform and periodic wall heat flux. The space under and above the bulk grain in the silo is free. A physical scaling of the problem leads us to build a dimensionless system of equations with three unusual numbers. An experimental study is carried out on a reduced silo filled with moistened mineral grain. The temperature and air moisture fields are investigated with thermocouples and sensors. Integration of equations allows us to evaluate natural convective velocity and quantity of water removed. Two flowing configurations are deduced : during the first half period, when the heat flux is high, the main part of the heat and mass transfer takes place in a boundary layer at the wall and this layer is fed with fresh air from the bottom and from the top through a central aspiration. During the second half period, when the heat flow is low, the stored heat provides a convective flux of a chimney type.