A liquid layer draining on a heated inclined surface is subjected to both thermocapillary and surface-wave instabilities. The combined influence of these two instabilities result in the formation of waves at the interface or breaking of the film. Since these phenomena are highly nonlinear, they can not be analyzed fully using either a linear or a weakly nonlinear analysis; the full system is to be solved. Hence in the present study, we integrate the governing equations for conservation of mass, momentum and energy in three-dimensional form. Through extensive numerical experiments, an instability mechanism for the formation of rivulets in horizontal and vertical layers is examined.