I looked on heatsinkusa and could only see a $12.35 option for 4" wide cut to 4" length. I guess I didn't find the right one. Can you give me a link to the $5 one? I'd like to see and if it's right then I'll just tell people they could order those, though I think even cheaper options could turn up.
I see they have a 4" wide option with 2" high fins for $12. Maybe that is large if we want to stack them close together.
They also have 3.5 and 4.2" inch sizes with .75" high fins for about $4 and $5 respectively. If 3.5x4" is big enough, $4.36 is pretty cheap.
Those 2" high heatsinks are quite beefy. The site claims a thermal resistance of 1.4 degrees C/watt for a 3"x4" section (presumably with natural convection). With such a thermal resistance, it looks like you can dissippate the heat of 16 chips with a slow/quiet fan, or perhaps no fan at all.
I think that one is very good but a bit expensive. They actually rate it at 1.4deg/W for a 3" section. So if it were 4" it should be a bit better at 1.05. With 35C air and 32W we'd be looking at 1.05*32 + 35 = 66C. Even with a small fan it would be good. However, I'd prefer to see something cheaper than $12.35. It's crazy that the most costly single part involved is a chunk of metal. When I have time I'll do some extensive searching but if other want to scour the web for something suitable I'd welcome suggestions. We're looking for something 1.05C/W or less for about $5 or less.
edit: I just looked again. I don't think it's a problem to use a slightly over size heat sink. Their 4.8" one that would cost only $3.72 and provide 1.69C/W. Not quite as good but probably fine with a small fan or moderate air flow. 1.69*32+35 = 89C. So a fan is needed but may not have to spin hard.
There will be a 3 pin fan controller on board and temp sensor. The sensor won't be close to the ASICs (but in the middle between them) so will need some calibration to set an appropriate fan speed range.