The generation of heat in high-density electronics is concentrated in spots, not uniform. Here we account for this fundamental aspect as a phenomenon of heat conduction in a flat body, from a concentrated heat source to surface dissipation of heat to an external flow. To facilitate conduction through the body, the heat source is connected to the rest of the body (the blade) with a vein of considerably higher thermal conductivity. The architecture resembles a botanical leaf, in which the heat source deposits the heat current at the root of the vein, and the upper and lower surfaces of the leaf dissipate the heat current to the surrounding fluid flow. The optimal dimensions of this leaflike architecture are determined analytically and numerically: the blade length, width, and thickness, the vein cross-sectional area, and the global thermal conductance of the entire multiscale body. The optimized features are nondimensionalized and reported as power laws that show explicitly the design effect of external convection and the thermal conductivities of the vein and the blade. © 2009 American Institute of Physics.