The influence of fluid depth in a convection problem in which heating is nonuniform is studied. We consider
a vessel that has at the bottom a temperature distribution which has Gaussian shape in the transversal direction
and whose surface is open to the atmosphere. Coupled buoyancy and thermocapillary effects are taken into
account. The results confirm a stationary bifurcation and a prelude of an oscillatory one as has been observed
recently in convection with quasi-one-dimensional heaters.