Sandwich panels with two-dimensional metal cores can be used to carry structural load as well as dissipate heat through solid conduction and forced convection. This work attempts to uncover the nature of heat transfer in these lightweight systems, with emphasis on the effects of varying cell morphologies and cell arrangements. The types of cell shape and cell arrangement considered include regular hexagon, square with connectivity 4 or 3, and triangle with connectivity 6 or 4. Two analytical models are developed: corrugated wall and effective medium. The former models the cellular structure in detail whilst, the latter models the fluid saturated porous structure using volume averaging techniques. The overall heat transfer coefficient and pressure drop are obtained as functions of relative density, cell shape, cell arrangement, fluid properties, and overall dimensions of the heat sink. A two-stage optimization is subsequently carried out to identify cell morphologies that optimize the structural and heat transfer performance at specified pumping power and at lowest weight. In the first stage, the overall heat transfer performance is optimized against relative density. Regular hexagonal cells are found to provide the highest levels of heat dissipation. In the second stage, a constraint on stiffness is added. It is then found that, for panels with thin cores, triangular cells constitute the most compact and yet stiff heat sink design; however, for high heat flux scenarios, hexagonal cells outperform triangular and square cells.