A metallic assembly transfers heat from a hot surface in contact with a heat source to specially shaped air passageways where cooling air is blown through. The air passageways in the metal assembly are arranged with a large metal surface area in contact with the cooling air for efficient heat transfer with low resistance to air flow. The passageways are formed by stacks of streamlined posts alternating with fins. The alternating layers are formed separately, stacked together, compressed, and subjected to hot dip brazing. This melts a low melting layer of cladding metal between metal layers to form the assembly into an integral assembly with efficient heat transfer between layers with reduced manufacturing costs.