The influence of thermal conditions at the side walls on natural convective heat transfer and fluid flow in a rectangular duct with a heated bottom and a cooled top walls duct is examined by direct numerical simulation. It is numerically shown that natural convective heat transfer and fluid flow have unique and complicated situations depending greatly on thermal conditions at the side walls, the geometry and Rayleigh number. And it is clear that the effects of thermal boundary conditions at the side walls bring about complicated phenomena.