The turbulent convection in a dry Boussinesq fluid above a heated surface is studied in a domain of large aspect ratio and long duration. Large-eddy simulations are used to investigate the influence of the dynamical character of the lower boundary and the effect of cooling at the top on the growth of convective cells. The aim is to identify physical mechanisms that lead to the broadening of convective cells even under conditions where moisture processes play no role. Cooling at the top produces a vertically uniform heat-flux, and it acts to enhance the total kinetic energy of the whole now. Essentially, there are two competitive effects: first, the prescribed heat-flux at the upper (lower) boundary produces very warm (very cool) fluid that is forced to rise (sink). The resulting large temperature-fluctuations are transported by large-scale motions and cause broad temperature-variances independent of height. On the other hand, the strong turbulent mixing (mainly near the boundaries where the turbulent kinetic energy is maximum) tries to homogenize the now structure in such a way that the resulting temperature-distribution is uniform. Except directly close to the walls, horizontal and vertical temperature-gradients are reduced. Additionally, a trend to form an organized large-scale horizontal drift in one direction near the bottom and in the opposite direction near the top was found for runs without surface friction. This horizontal streaming motion has two effects: firstly, the turbulent mixing is enhanced due to larger shear and, secondly, separated thermals approach faster and are able to merge more easily, forming gradually growing cells. An adiabatic upper boundary condition leads to a heat-nux profile that is linear and decreasing with height, and to a moderate temporal growth of thermal structures. A considerable scale-reduction of the temperature structures occurs because of friction at the lower surface.