The purpose of the present work was to investigate numerically the effect of the top and/or bottom blind openings on the convective heat transfer from a window fitted with a double-layered top down-bottom up honeycomb blind system. Top down-bottom up systems that utilize so-called honeycomb (or cellular) blinds can be opened at the top and/or the bottom. When a honeycomb blind is fully closed there are two or more vertical blind portions and a series of horizontal or nearly horizontal blind portions which join the vertical portions and form a column of cells. This gives the blind system its honeycomb or cellular structure. When opening a honeycomb blind the vertical portions of the blind bend or fold allowing the overall height of the blind to decrease. A double-layered honeycomb blind is constructed with three vertical blind portions and two columns of cells. A recessed window has been considered in the present study and only the convective heat transfer from the window to the surrounding room has been investigated. The surfaces of the blind are assumed to offer no resistance to heat transfer. The commercial CFD solver ANSYS FLUENT© has been used to obtain the solution. Over the range of parameters considered in this study, both laminar and turbulent flow can occur. The k-ε turbulence model has been used in obtaining the solutions. The convective heat transfer rate from the inner surface of the window, expressed in terms of a mean Nusselt number based on the window height and the difference between the window and the air temperatures, will depend on the Rayleigh number, also based on the window height, and the difference between the window and the air temperatures, the dimensionless top and bottom blind openings, and the dimensionless window recess depth. Variations of the mean Nusselt number with Rayleigh number for various values of these other parameters have been obtained and the results used to study how these other parameters affect the window heat transfer rate.