We consider the dynamics of an Boussinesq approximation Benard
convection uid evolving in a three-dimensional domain bounded below by a
xed atten boundary and above by a free moving surface. The domain is
horizontally periodic and the eect of the surface tension is neglected
on the free surface. By developing a priori estimates for the model, we
prove the global existence and almost exponential decay of solutions in
the framework of high regularity.