Copper can be very usefull to use as a backing bar when welding thin materials partiularly stainless steel, it will conduct the heat away into itself and act as a chill, this will help to reduce the amount of distortion, make sure the copper chill is in close contact and that the mating sufaces are clean to avoid weld contamination, aluminium and to a lesser degree, brass can be used, but if the arc touches them you risk root contamination, ok to back up on a lap weld though.
I understand reasoning for using a heat sink, if it is just to eliminate too much root penetration, use ceramic tiles, no hassle, no contamination either.
This link will give you more understanding on the above katfish.
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Ive used those ceramic backing tiles when building stainless steel pressure vessels for the chemical industry, a bit fiddly to use and not cheap, but the trough traps the shielding gas and gives a similar effect to back purging,