The hydroelectric dams are taking energy from the water system by slowing its descent. Presumably the friction of faster moving water would heat the riverbeds and surroundings more than the waste heat from the data centers does. The thermal impact should be negligible compared to releasing energy stored in hydrocarbons or atoms. However, pouring a lot of concrete can release enormous amounts of carbon dioxide.
> Presumably the friction of faster moving water would heat the riverbeds and surroundings more than the waste heat from the data centers does
I would be seriously surprised about that. Do you have some data about heat leaked to the sorroundings by water friction?
I would say the potential energy of water is mostly carried by the water itself to its final destination, by slowly heating up during descent. The surroundings are not appreciably heated, since water is a good coolant.
So let's picture a waterfall: water practically stops at the bottom, so potential energy has dissipated somehow, but surroundings are not heated, water is. The energy remains in the water, which continues its happy descent to the sea.
We were thinking along similar lines. Except I just had an amusing observation about how I'm seeing some people telling me the Arctic might melt due to technological activity and another where critical datacenters are being built in the Arctic. One better hope the other isn't right. ;)