Here's my step-by-step for the home made heatsink.
I worked out (by adding to a pile of pennies on the CM3 chip until the case top was just proud) that the heatsink needed to be 12mm deep, and the size of the chip is 14mm square.
I ordered three things from eBay, for a total cost of about £7.50: a small piece of 0.5mm thick copper sheet, some thermal grease, and a pack of epoxy resin.
I then marked out the copper sheet into 14mm squares, and cut it up with a pair of snips. Then degrease all the pieces of copper, the inside of the Slice case top, and the top of the CM3 chip with isopropyl alcohol.
Next make a stack of the copper pieces, sandwiched with thermal grease. I needed 17 pieces of copper to achieve the required 12mm height.
Next I worked out the position in the Slice case top, and stuck the heatsink into position with thermal grease. Then with the epoxy resin, I "drizzled" a little of the glue onto the sides of the heatsink to hold it all together, and finally used the epoxy to glue the heatsink to the inside of the case top. This is what the final result looked like:
The very last stage was to apply thermal grease to the bottom of the heatsink, and then assemble the case. When I put the case together by resting it in position, the case was split by about 0.5mm, and when bolted together this slack is easily taken up my the flexibility of the CM3 in its socket.
As for temperatures, before the heatsink (and without the case top) the CM3 idled at 54 degrees, and under heavy load was reaching 85 degrees, and throttling the CPU back to 600MHz. With the heatsink the idle temperature is about 42 degrees, and under load maxes out at 48-50 degrees, with no sign of the on-screen thermometer.